1. She is excited about the wedding.
'about' is probably the the most usual preposition to go with 'excited' . The wedding is a planned occasion in the future which she is really looking forward to.
2. We are excited by the prospect of a party.
This indicates our reaction to an idea. You could also use 'at' here.
3. They are excited for the summer.
This sentence does not make a lot of sense. It would be correct to use 'about' here, if you mean that there is something special planned for the summer, and they are looking forward to it.
The only instance I can think of where it would be correct to use 'excited for' is if someone tells you some good news about something exciting that they are going to do, and you would say to them eg 'That's great, I'm so excited for you!'. This would mean 'I'm excited on your behalf'.