1. For the Conductor, a psalm by David,
2. when Nathan the prophet came to him after he had gone to Bathsheba.
3. Be gracious to me, O God, in keeping with Your kindness; in accordance with Your abounding compassion, erase my transgressions.
4. Cleanse me thoroughly of my wrongdoing, and purify me of my sin.
5. For I acknowledge my transgressions, and my sin is always before me.

Tehillim Ohel Yoseph Yitzchok (Kehot Publication Society)

Tehillim is recited by Jewish people collectively and individually, as the desire occurs to offer praise and thanksgiving to G-d; or alternitavely, in times of crisis and need, as a form of supplication, and even as a venue to express regret for sin.

6. Against You alone have I sinned, and done that which is evil in Your eyes; [forgive me] so that You will be justified in Your verdict, vindicated in Your judgment.
7. Indeed, I was begotten in iniquity, and in sin did my mother conceive me.
8. Indeed, You desire truth in the innermost parts; teach me the wisdom of concealed things.
9. Purge me with hyssop and I shall be pure; cleanse me and I shall be whiter than snow.
10. Let me hear [tidings of] joy and gladness; then the bones which You have shattered will rejoice.
11. Hide Your face from my sins, and erase all my trespasses.
12. Create in me a pure heart, O God, and renew within me an upright spirit.
13. Do not cast me out of Your presence, and do not take Your Spirit of Holiness away from me.
14. Restore to me the joy of Your deliverance, and uphold me with a spirit of magnanimity.
15. I will teach transgressors Your ways, and sinners will return to You.
16. Save me from bloodguilt, O God, God of my deliverance; my tongue will sing Your righteousness.
17. My Lord, open my lips, and my mouth shall declare Your praise.
18. For You do not desire that I bring sacrifices, nor do You wish burnt offerings.
19. The offering [desirable] to God is a contrite spirit; a contrite and broken heart, God, You do not disdain.
20. In Your goodwill, bestow goodness upon Zion; rebuild the walls of Jerusalem.
21. Then will You desire sacrifices [offered in] righteousness, olah and other burnt offerings; then they will offer bullocks upon Your altar.