I can't describe it, but the scriptures can.
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As I was thus racked with torment...I remembered also to have heard...concerning the coming of one Jesus Christ, a Son of God, to atone for the sins of the world.
Now as my mind caught hold upon this though, I cried within my heart: O Jesus, thou Son of God, have mercy on me, who am in the gall of bitterness, and am encircled about by the everlasting chains of death[!]
And now, behold, when I thought this I could remember my pains no more; yea, I was harrowed up by the memory of my sins no more.
AND OH, WHAT JOY, AND WHAT MARVELOUS LIGHT I DID BEHOLD; YEA, MY SOUL WAS FILLED WITH JOY AS WAS EXCEEDING AS WAS MY PAIN!
Alma 36:17-20
I will love thee, O Lord, my strength.
The Lord is my rock, and my fortress, and my deliverer; my God, my strength, in whom I trust;
The sorrows of death compassed me, and the floods of ungodly men made me afraid. The sorrows of hell compassed me about: the snares of death prevented me.
In my distress I called upon the Lord, and cried unto my God: he heard my voice... and my cry came before him, even into his ears.
He sent from above, he took me, he drew me out of many waters.
He delivered me from my strong enemy, and from them which hated me: for they were too strong for me. They prevented me in the day of my calamity: but the Lord was my stay.
The Lord rewarded me according to my righteousness; according to the cleanness of my hands hath he recompensed me.
Ps. 18: 1-2, 4-6, 16-18, 20.
"Blessed be the name of our God; let us sing to his praise, yea, let us give thanks to his holy name, for he doth work righteousness forever.
My heart is brim with joy, and I will rejoice in my God.
...I do not boast in my own strength nor in my own wisdom; but behold, my joy is full, yea my heart is brim with joy, and I will rejoice in my God! Yea, I know that I am nothing; as to my strength I am weak; therefore I will not boast of myself, but I will boast of my God, for in his strength I can do all things;
[We] are brought to sing redeeming love, and thus because of the power of his word which is in us, therefore, have we not great reason to rejoice?
Therefore let us glory, yea, we will glory in the Lord. yea, we will rejoice, for our joy is full; yea, we will praise our God forever. Behold, who can glory too much in the Lord? yea who can say too much of his great power, and of his mercy, and of his long-suffering towards the children of men? Behold I say unto I cannot say the smallest part of what I feel!
Alma 26: 8, 10-13, 16
Thou wilt shew me the path of life: in thy presence is fulness of joy; at thy right hand there are pleasures evermore.
And my soul shall be joyful in the Lord: it shall rejoice in his salvation.
Ps. 16:11; 34: 9.
How is it done? The Savior said:
"Come unto me, all ye that labour and our heavy laden, and I will give you rest.
Take my yoke upon you, and learn of me; for I am meek and lowly in heart. and ye shall find rest unto your souls. For my yoke is easy and my burden is light.
Matthew 11: 28-30
"...your sorrow shall be turned into joy. In the world your joy is not full, but in me your joy is full. My spirit... shall fill your soul with joy. "
John 16:20; D&C 101:36; D&C 11:13
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For the promise is that if we draw near unto Him, He will draw near unto us. When we seek Him, we WILL find him. (D&C 88: 63).
