(つぐなう) To compensate someone for bad stuff you did. This is used in everyday life, and can take various forms:doing their homework or baking them a cake, It’s more of a sincere expression of regret than 弁償..
する(べんしょうする) To compensate financially, because of a lawsuit. More of a formal/legal term than 償う.
わせ(うめあわせ) To compensate yourself. Like, he grows his hair long in back to compensate for going bald in front. He bought a SUV to compensate for having a small dick.