Formal:
* Удачи! (Udachi!) - This is the most common and versatile way to say "good luck". It literally means "good luck" and can be used in most situations.
Informal:
* Ни пуха, ни пера! (Ni puha, ni pera!) - This is a more playful and idiomatic expression. It literally means "neither down nor feather!", and is believed to bring good luck. It is often used when someone is about to take an exam or perform on stage. The person you are wishing good luck to is supposed to reply "К черту!" (K chertu!) which means "To the devil!" to avoid bad luck.
* Везения! (Vezeniya!) - This literally means "luck" and is a less formal way to say "good luck".
* Счастливого пути! (Schastlivogo puti!) - This means "Happy journey!" and is often used when someone is leaving on a trip.
You can also say "good luck" in a more specific way, depending on the situation. For example, you could say:
* Пусть все получится! (Pust' vse poluchitsya!) - This means "May everything work out!"
* Успехов! (Uspekhov!) - This means "Success!"
The best way to choose the right phrase depends on the context of the situation and your relationship with the person you are speaking to.