From Jonathan Edwards's "Advice to Young Converts":

Under special difficulties, or when in great need of or great longings after particular mercies for your self or others, set apart a day of secret fasting and prayer alone. Let the day be spent not only in petitions for the mercies you desired, but in searching your heart, and looking over your past life, and confessing your sins before God, not as practiced in public prayer, but by a very particular rehearsal before God. Include the sins of your past life from your childhood up until now, both before and after conversion, with particular circumstances and aggravations. Also be very particular and as thorough as possible, spreading all  the abominations of your heart before him. 

Jonathan Edwards reminds us that our motivation to serve Christ should not be fear, but our desires, our affections, our loves. The following is from "Advice to Young Converts" (emphasis mine): 

When the exercise of grace is at a low ebb, and corruption prevails, and by that means fear prevails, don't desire to have fear cast out any other way than by the reviving and prevailing of love, for it is not agreeable to the method of God's wise dispensations that it should be cast out any other way. When love is asleep, the saints need fear to restrain them from sin, and therefore it is so ordered that at such times fear comes upon them, and that more or less as love sinks. But when love is in lively exercise, persons don't need fear. The prevailing of love in the heart naturally tends to cast out fear as darkness in a room vanishes away as you let more and more of the perfect beams of the sun into it: "There is no fear in love. But perfect love drives out fear, because fear has to do with punishment. The one who fears is not made perfect in love." (1 John 4:18)

From Jonathan Edwards' "Advice to Young Converts":

Be always greatly humbled by your remaining sin, and never think that you lie low enough for it, but yet don't be at all discouraged or disheartened by it. Although we are exceedingly sinful, we have an advocate with the Father, Jesus Christ the righteous, the preciousness of whose blood, the merit of whose righteousness, and the greatness of whose love and faithfulness infinitely overtop the highest mountains of our sins.

It is a wonderful thing when God begins to give us those sweet longings after Christ. One young man who had these longings was Jonathan Edwards. As a college student, Jonathan Edwards lived as if he was a Christian, but he was just going through the motions, with a sense of self-righteousness. Then, to his surprise, he found that God was awakening him to Himself. The following is from his Personal Narrative (I have edited this excerpt for clarity and for length).

The first instance that I remember of an inward, sweet delight in God and divine things was on reading I Tim. 1:17: Now unto the King eternal, immortal, invisible, the only wise God, be honour and glory for ever and ever, Amen. As I read the words, there came into my soul a sense of the glory of God; a new sense, different from any thing I ever experienced before. Never did any words of scripture move me as these words did. I thought with myself, how excellent a Being that was, and how happy I should be, if I could enjoy that God, and be rapt up to him in heaven, and be swallowed up in him for ever! I kept saying and singing over these words of scripture to myself; and I went to pray to God that I might enjoy him, and prayed in a manner different from what I used to; now I prayed with a new sort of affection.

From about that time, I began to have a new kind of apprehensions and ideas of Christ and the work of redemption, and the glorious way of salvation by him. An inward, sweet sense of these things came into my heart at times; and my soul was led away in pleasant views and contemplations of them. And my mind was greatly engaged to spend my time in reading and meditating on Christ, on the beauty and excellency of his person, and the lovely way of salvation by free grace in him. I found, from time to time, an inward sweetness, that would carry me away, in my contemplations. This I know not how to express otherwise, than by a calm, sweet escape in my soul from all the concerns of this world; and sometimes a kind of vision, or imagination, of being alone in the mountains, or some solitary wilderness, far from all mankind, sweetly conversing with Christ, and swallowed up in God. The sense I had of divine things would suddenly flame up within me, a sweet burning in my heart, an ardor of soul, that I know not how to express.

After this my sense of divine things gradually increased, and became more and more lively, and had more of that inward sweetness. The appearance of everything was altered. There seemed to be a calm sweet cast, or appearance of divine glory, in almost everything. God's excellency, his wisdom, his purity and love, seemed to appear in everything; in the sun, moon, and stars; in the clouds, and blue sky; in the grass, flowers, trees; in the water, and all nature; which used greatly to fix my mind. I often used to sit and stare at the moon; and in the day, I spent much time watching the clouds and sky, to behold the sweet glory of God in these things; in the mean time, I was singing forth, with a low voice my contemplations of the Creator and Redeemer.
I felt great satisfaction in these things, but that did not content me. I had vehement longings of soul after God and Christ, and after more holiness, wherewith my heart seemed to be full, and ready to break. These longings often brought to my mind the words of the Psalmist in Psalm 119:28: My soul breaketh for the longing it hath. I often felt a mourning and lamenting in my heart, that I had not turned to God sooner, that I might have had more time to grow in grace. My mind was greatly fixed on divine things; almost perpetually in the contemplation of them. I spent most of my time in thinking of divine things, year after year; often walking alone in the woods, and solitary places, for meditation, soliloquy, and prayer, and communion with God. Prayer seemed to be natural to me, as the breath by which the inward burnings of my heart had vent.

The delights which I now felt in the things of religion, were of an exceeding different kind from those before mentioned, that I had when a boy; and what I then had no more notion of, than one born blind has of pleasant and beautiful colors. They were of a more inward, pure, soul animating and refreshing nature. Those former delights never reached the heart; and did not arise from any sight of the divine excellency of the things of God; or any taste of the soul satisfying and life­giving good there is in them.

Resolved, to endeavor to obtain for myself as much happiness in the other world as I possibly can, with all the power, might, vigor, and vehemence, yea violence, I am capable of, or can bring myself to exert, in any way that can be thought of.

Jonathan Edwards, Resolutions

Persons need not and ought not to set any bounds to their spiritual and gracious appetites. [Instead, they should] be endeavoring by all possible ways to inflame their desires and to obtain more spiritual pleasures. . . . Our hungerings and thirstings after God and Jesus Christ and after holiness can't be too great for the value of these things, for they are things of infinite value. . . . [Therefore] endeavor to promote spiritual appetites by laying yourself in the way of allurement. . . . There is no such thing as excess in our taking of this spiritual food. There is no such virtue as temperance in spiritual feasting.

Jonathan Edwards, quoted in When I Don't Desire God, John Piper

For as God is infinitely the greatest Being, so he is allowed to be infinitely the most beautiful and the most excellent: and all the beauty to be found throughout the whole universe is but the reflection of the diffused beams of that Being who hath an infinite fulness of brightness and glory; God . . . is the foundation and fountain of all being and beauty.

Jonathan Edwards, The Nature of True Virtue