I'm studying the laws of Lashon Hara (gossip, slander) I took upon myself. How do we do Teshuva for speaking Lashon Hara? And how do we become more careful with our speech?

Fantastic- I really admire your idealism and self-discipline! Proper teshuva for lashon hara, in addition to asking mercy from God, also includes asking forgiveness from the person whom we spoke against. The problem is, when we ask their forgiveness, we inadvertently are hurting them once again, which is the last thing we want to do! The best solution is to utilize the Yom Kippur spirit, when at that time, everyone is asking forgiveness of each other, and accordingly, the person won’t be hurt. The best way to be more careful is exactly what you’re doing, to study the laws regularly, and eventually we internalize that which we learn.