By human testimony only

Joseph Smith wrote the following in "Lectures on Faith":

Q. What testimony have men, in the first instance, that there is a God?
A. Human testimony, and human testimony only (see Lecture 2:56).
Q. What excited the ancient saints to seek diligently after a knowledge of the glory of God, his perfections, and attributes?
A. The credence they gave to the testimony of their fathers (see Lecture 2:56).
Q. How do men obtain a knowledge of the glory of God, his perfections, and attributes?
A. By devoting themselves to his service, through prayer and supplication incessantly, strengthening their faith in him, until like Enoch, the Brother of Jared, and Moses, they obtain a manifestation of God to themselves (see Lecture 2:55).
Q. Is the knowledge of the existence of God a matter of mere tradition, founded upon human testimony alone, until persons receive a manifestation of God to themselves?
A. It is.

Joseph described how mankind from Adam to Noah were acquainted with either men who knew God personally or men who knew them personally, enabling all mankind to be aware of the existence and attributes of God, and of the details of the gospel plan of salvation.

It may be disturbing to some to recognize that the path to salvation requires the intercession of beings other than God. This is disturbing if we confine our understanding of their role to what some sects of Christianity teach: that the authority of men is required. Intercession is very different from authority. The Lord taught plainly that the inclination of all mankind is to exert dominance over his fellowmen. The Lord's power and authority, however, are most plainly manifested not in dominance, but in submission. The dominion of men is force, the dominion of God is condescension. Men display power through violence, God displays it through long suffering. The might of men is found in armies, money, and goods. The might of God is found in his reaction to every hammer blow to the nails in his hands, and each lash he received as punishment for his attempt to reach us. He has an exuberant willingness to come down to our level to individually bless us with forgiveness, mercy, and blessings that far exceed our gratitude for or use of them.

When we believe that men's authority is required to save us, we set up certain individuals with dominion over us. We trust that whatever they tell us is God's word, and whatever they tell us to do is God's will. They become the source of truth for us. This is abominable idolatry. No matter what stature the idols have achieved with God, it can never bring you more than the glory of angels in the best case. In the worst case, it will lead you straight to hell.

When we understand that the intercession of men (and angels) is required to save us, we retain our focus on the Lord Jesus, the source of all truth. Just as a pipe retains the capacity to carry poisoned water no matter how much clean water it previously carried, men are, at best, only unreliable messengers of truth. Their necessity is a blessing from God, as it gives each individual the opportunity to mimic, on an infinitesimally small scale, the intercession the Lord Jesus works for us with the Father: they obtain more light and truth than we merit in our lower state, and they dispense it, satisfying the demands of justice through their condescending sacrifice.

22 For behold, God knowing all things, being from everlasting to everlasting, behold, he sent angels to minister unto the children of men, to make manifest concerning the coming of Christ; and in Christ there should come every good thing.
23 And God also declared unto prophets, by his own mouth, that Christ should come.
24 And behold, there were divers ways that he did manifest things unto the children of men, which were good; and all things which are good cometh of Christ; otherwise men were fallen, and there could no good thing come unto them.
25 Wherefore, by the ministering of angels, and by every word which proceeded forth out of the mouth of God, men began to exercise faith in Christ; and thus by faith, they did lay hold upon every good thing; and thus it was until the coming of Christ. (Moroni 7)

The pattern is the same as that worked by the Lord, even if the magnitude is exceptionally different.

Those who cut themselves off from the mortal channel of truth cut themselves off from the Lord, yet those who accept falsehood will also cut themselves off from the Lord. The stakes are high. How can we know what we receive is good or evil?

One way we can know is to "try the spirits" (1 John 4:1):

28 Now, we will compare the word unto a seed. Now, if ye give place, that a seed may be planted in your heart, behold, if it be a true seed, or a good seed, if ye do not cast it out by your unbelief, that ye will resist the Spirit of the Lord, behold, it will begin to swell within your breasts; and when you feel these swelling motions, ye will begin to say within yourselves—It must needs be that this is a good seed, or that the word is good, for it beginneth to enlarge my soul; yea, it beginneth to enlighten my understanding, yea, it beginneth to be delicious to me.
29 Now behold, would not this increase your faith? I say unto you, Yea; nevertheless it hath not grown up to a perfect knowledge.
30 But behold, as the seed swelleth, and sprouteth, and beginneth to grow, then you must needs say that the seed is good; for behold it swelleth, and sprouteth, and beginneth to grow. And now, behold, will not this strengthen your faith? Yea, it will strengthen your faith: for ye will say I know that this is a good seed; for behold it sprouteth and beginneth to grow.
31 And now, behold, are ye sure that this is a good seed? I say unto you, Yea; for every seed bringeth forth unto its own likeness.
32 Therefore, if a seed groweth it is good, but if it groweth not, behold it is not good, therefore it is cast away.
33 And now, behold, because ye have tried the experiment, and planted the seed, and it swelleth and sprouteth, and beginneth to grow, ye must needs know that the seed is good. (Alma 32)

Faith, hope, charity. Faith is belief in a true principle sufficient to conform to it in thought and action. Hope, in the sense used with faith and charity, is to receive promises from God and then conform one's thought and actions to the eventuality of the fulfillment of the promise. Charity is caring for others the way that God cares for them. These three interrelated topics work together to frame the pathway to a habitation with God.

Faith comes through hearing. What does that actually mean? It is simply describing the pattern that I laid out above: Some men are closer to God than others. They have obtained more light and truth, and their mission in this world is to condescend and give it to others through their own sacrifice. They experience, then they relate.

We know this is true, because it was told by someone who saw it happen. Now you can have faith too. (John 19:35, CEV)

The predominant LDS-inspired idea of dispensations is mostly rubbish. This concept states that, from time to time, God sends a special person to the earth to be the connection to God, or through whom he will uniquely deliver truth to his children. Instead, we ought to imagine truth as something like a radio signal, with every person on the earth being tuned to receive it to a greater or lesser extent. If we find ourselves completely tuned out, it takes the help of someone who is tuned in more than us to get our initial tuning. If we were capable of achieving a better tuning in and of ourselves, we would have done so already. If someone presents with a better tuning than ours—a clearer, louder signal—we ought to see what we can learn from them about how to improve our own tuning. At any given time, there is going to be one person with a better tuning than anyone else, but the only thing stopping anyone else from having the same tuning is their own actions.

Even though God has a kingdom, we err when we make too direct a comparison to the kingdoms of this world. After all, he said his kingdom was not of this world. God's light and truth is accessible to anyone, at any time, subject to the same conditions: heed and diligence. Any who exercise more heed and diligence than their fellows will end up with more light and truth than they have. Those who have obtained have a responsibility to dispense it to others.

1 ...I would that ye should remember that the Lord God ordained priests, after his holy order, which was after the order of his Son, to teach these things unto the people.
2 ...that thereby the people might know in what manner to look forward to his Son for redemption.
3...being called and prepared from the foundation of the world according to the foreknowledge of God, on account of their exceeding faith and good works; in the first place being left to choose good or evil; therefore they having chosen good, and exercising exceedingly great faith, are called with a holy calling, yea, with that holy calling which was prepared with, and according to, a preparatory redemption for such.
4 And thus they have been called to this holy calling on account of their faith, while others would reject the Spirit of God on account of the hardness of their hearts and blindness of their minds, while, if it had not been for this they might have had as great privilege as their brethren.
5 Or in fine, in the first place they were on the same standing with their brethren; thus this holy calling being prepared from the foundation of the world for such as would not harden their hearts, being in and through the atonement of the Only Begotten Son, who was prepared—
6 And thus being called by this holy calling, and ordained unto the high priesthood of the holy order of God, to teach his commandments unto the children of men, that they also might enter into his rest—
10 Now, as I said concerning the holy order, or this high priesthood, there were many who were ordained and became high priests of God; and it was on account of their exceeding faith and repentance, and their righteousness before God, they choosing to repent and work righteousness rather than to perish;
11 Therefore they were called after this holy order, and were sanctified, and their garments were washed white through the blood of the Lamb.
12 Now they, after being sanctified by the Holy Ghost, having their garments made white, being pure and spotless before God, could not look upon sin save it were with abhorrence; and there were many, exceedingly great many, who were made pure and entered into the rest of the Lord their God.
13 And now, my brethren, I would that ye should humble yourselves before God, and bring forth fruit meet for repentance, that ye may also enter into that rest.
14 Yea, humble yourselves even as the people in the days of Melchizedek, who was also a high priest after this same order which I have spoken, who also took upon him the high priesthood forever.
16 Now these ordinances were given after this manner, that thereby the people might look forward on the Son of God, it being a type of his order, or it being his order, and this that they might look forward to him for a remission of their sins, that they might enter into the rest of the Lord.
17 Now this Melchizedek was a king over the land of Salem; and his people had waxed strong in iniquity and abomination; yea, they had all gone astray; they were full of all manner of wickedness;
18 But Melchizedek having exercised mighty faith, and received the office of the high priesthood according to the holy order of God, did preach repentance unto his people. And behold, they did repent; and Melchizedek did establish peace in the land in his days; therefore he was called the prince of peace, for he was the king of Salem; and he did reign under his father.
21 And now it came to pass that when Alma had said these words unto them, he stretched forth his hand unto them and cried with a mighty voice, saying: Now is the time to repent, for the day of salvation draweth nigh;
22 Yea, and the voice of the Lord, by the mouth of angels, doth declare it unto all nations; yea, doth declare it, that they may have glad tidings of great joy; yea, and he doth sound these glad tidings among all his people, yea, even to them that are scattered abroad upon the face of the earth; wherefore they have come unto us.
23 And they are made known unto us in plain terms, that we may understand, that we cannot err; and this because of our being wanderers in a strange land; therefore, we are thus highly favored, for we have these glad tidings declared unto us in all parts of our vineyard.
24 For behold, angels are declaring it unto many at this time in our land; and this is for the purpose of preparing the hearts of the children of men to receive his word at the time of his coming in his glory.
25 And now we only wait to hear the joyful news declared unto us by the mouth of angels, of his coming; for the time cometh, we know not how soon. Would to God that it might be in my day; but let it be sooner or later, in it I will rejoice.
26 And it shall be made known unto just and holy men, by the mouth of angels, at the time of his coming, that the words of our fathers may be fulfilled, according to that which they have spoken concerning him, which was according to the spirit of prophecy which was in them.
27 And now, my brethren, I wish from the inmost part of my heart, yea, with great anxiety even unto pain, that ye would hearken unto my words, and cast off your sins, and not procrastinate the day of your repentance;
28 But that ye would humble yourselves before the Lord, and call on his holy name, and watch and pray continually, that ye may not be tempted above that which ye can bear, and thus be led by the Holy Spirit, becoming humble, meek, submissive, patient, full of love and all long-suffering;
29 Having faith on the Lord; having a hope that ye shall receive eternal life; having the love of God always in your hearts, that ye may be lifted up at the last day and enter into his rest.
30 And may the Lord grant unto you repentance, that ye may not bring down his wrath upon you, that ye may not be bound down by the chains of hell, that ye may not suffer the second death.
31 And Alma spake many more words unto the people, which are not written in this book. (Alma 13)