In his sermon on Jeremiah 3 (Jeremiah and Lamentations), Philip Graham Ryken lays out four aspects of true (as opposed to sham) repentance.

First, repentance must be wholehearted. “The believer’s relationship with God is a love-relationship. Redemption is a romance; true love requires an undivided heart” (56).

Second, repentance is God-directed.

Only acknowledge your guilt,
that you rebelled against the LORD your God
and scattered your favors among foreigners
under every green tree,
and that you have not obeyed my voice,
declares the LORD. Jeremiah 3:13

Repentance must be directed toward God. It must justify God’s judgment, “Only acknowledge your guilt.” Repentance is not based upon an argument that I am not so bad, therefore, God should forgive me. Rather, repentance says, I am so evil that I need forgiveness:

For your name’s sake, O LORD,
pardon my guilt, for it is great. Psalm 25:11

Third, true repentance is grace-responsive. The call for repentance begins with the offer of God’s grace:

Go, and proclaim these words toward the north, and say,
“‘Return, faithless Israel,
declares the LORD.
I will not look on you in anger,
for I am merciful, declares the LORD;
I will not be angry forever. Jeremiah 3:12

Or do you presume on the riches of his kindness and forbearance and patience, not knowing that God’s kindness is meant to lead you to repentance? Romans 2:4

“[God] had every right to slam the door on your forever. But he is your loving, merciful, all-suffering husband. He keeps on welcoming you back home” (57).

Fourth, true repentance will produce obedience, it is “obedience-producing.

In Psalm 51, David prays out his repentance. He then prays that he will “teach transgressors your ways” (v. 13); and will offer praise to God (v. 15). John the Baptist instructs the people, “Bear fruit in keeping with repentance” (Matt. 3:8).

The Lord himself warned:

21 “Not everyone who says to me, ‘Lord, Lord,’ will enter the kingdom of heaven, but the one who does the will of my Father who is in heaven.
22 On that day many will say to me, ‘Lord, Lord, did we not prophesy in your name, and cast out demons in your name, and do many mighty works in your name?’
23 And then will I declare to them, ‘I never knew you; depart from me, you workers of lawlessness.’ Matthew 7:21-23

Thus, repentance begins with the grace of God, which brings a turning to God. In the turning to God there is a transformation: grace produces obedience.