Formal:
* 祝你好运 (zhù nǐ hǎo yùn): This is the most common and formal way to say "good luck". It literally means "wish you good fortune".
Informal:
* 好运 (hǎo yùn): This is a more casual way to say "good luck", meaning "good fortune".
* 加油 (jiā yóu): This literally means "add oil", but it's used as an expression of encouragement and support, similar to "go get 'em" or "good luck".
* 一切顺利 (yīqiè shùnlì): This means "everything goes smoothly", and is a polite way to wish someone luck.
Other expressions:
* 心想事成 (xīnxiǎng shìchéng): This means "may your wishes come true", and is a more poetic way to say "good luck".
* 旗开得胜 (qí kāi dé shèng): This literally means "the flag opens with victory", and is used to wish someone success in a competition or a new venture.
The best way to choose the right expression is to consider the situation and your relationship with the person you are talking to.