Teshuvah means to repent of something inappropriate you have done, and to resolve not to do it again.
Some tips on how to do it:
1) Say it out loud. At night, or some time when you are alone, say out loud: “Dear God, I am sorry for the sin I committed before You by [and here goes what you did]. There is a specific prayer in prayer books called vidui (Confession) that we say on Yom Kippur. You can say it and add this line anywhere. When you hear your own voice saying how sorry you are for what you did, you feel it much more deeply.
2) Make amends for what you did. Apologize and compensate whoever was affected by your mistake. If your sin was directed toward someone else, it wouldn't be fair for God to forgive you without involving that other person. If they don't forgive you at first, keep trying until they become unreasonable. At that point, you've done what was expected of you, and now it's the other party's responsibility.
3) Charity. Simply give more money than you were used to giving. Sin diminishes divine vitality on earth. Charity heals the world and your soul and replenishes that missing energy in the universe.
4) Move forward in life. Make amends for what happened. Be better, act better, study more, etc. Sin creates a kind of inertia that drags you down further and further. That inertia must be broken, and the way to do so is to increase your observance of Torah and Mitzvot.
Repentance (Teshuvah) is powerful, but of course, we don't sin only to repent later. According to our sages, however, a sin can elevate you more than all the mitzvot you could perform in life if you repent out of love—love for God, for His Torah, and for your soul.