Children fall out and make up all the time and in the main, it's usually best to let them find their own way with respect to friendships. However, having said that, there are discussions you can have with your child that will help them maintain their relationships.
Something some children do that isn't helpful, is called 'splitting'. What this means is that a child's opinion of someone is as good as the impact of their last interaction with that person. In other words, when someone has been mean to them, that person is simply 'bad' with no consideration that there might have been a reason why the person did what they did (e.g. they were tired, they were in a bad mood because they had just been told off etc). Splitting tends to prevent children from attempting to make up after falling out as they simply hold on to the idea that the other person is not worth having as a friend. The breakdown in the friendship will still be causing them upset however.
To help children do splitting less and to encourage them to attempt to 'make up:
1) Let you child tell you how the incident made them feel and validate those feelings.
2) Ask you child to think about the friendship. What do they like about the other person and what do they enjoy doing with that person? Make it clear that the friend is still the same child they were recently good friends with.
3) Ask your child to consider why the person might have behaved the way they did. Ask your child to think of reasons why their friend might have behaved the way they did. (e.g. tired or hungry, upset by something they had done, having a hard time elsewhere etc).
4) Ask your child to imagine them being friends again and what that feels like.
5) Set your child the challenge of making up. Can they use 'I messages' to explain how they felt and can they say clearly to their friend that they want things to be sorted and for everyone to feel good again.