you have to give them some time before trying to make up- some people have to calm down before seeing their ex-friend. try to say sorry and if that doesn't go to plan, show them that you mean it, and that could mean doing something that you have never to before that they like, e.g. swimming 10 metres or if their birthday is coming up, surprise them. they are lots of ways to make up but somethings there is a time for things to happen.
When trust has been broken or altered in a friendship, it is important that the person who broke their friends trust apologizes and makes sure that they are stable enough to not make the same decisions again. they must make sure they communicate how they feel about the situation, including the person who was hurt. it is hard to be a perfect friend, and we all make mistakes. as long as a friend knows that there will not be another again and that they are remorseful and sorry for their actions, and there is good change shown in their behavior then it is okay to assume friendship again
It depends on your relationship with him/her. Probably say something like, "Thank you for being an inspiration", or "Thanks for being so patient". Anything you think you want to say.
