How to say "I'm finished"?
Depend on the context, 好 and/or 完 can be used.

好 is more oral friendly as there is no emphasize of any difference between the speaker and the listener. In some cases, using 好 may show a closer relation between the parties of conversation than 完.

On the other hand, 完 is more formal. It is a better parallel to "finish" comparing to 好 as the latter has broader usage. Be weary while using 完 as it is often used when the parties involved in conversion are not equal.

For instance, 完 is used when your boss speaks to you, your teacher speaks to you, your group leader speaks to you, etc. 好 on the other hand, tend to be used when your friend speaks to you, your partner speaks to you, etc.