When you have a method, you have a specific way of doing something, or a certain plan or process for getting something done. Your method of doing something might be different from somebody else's, but your method is a way that works well for you that you've thought about carefully and practiced many times.
I follow this method for serving an avocado: slice it in half with a knife, then use a spoon to scoop out all the deliciousness. That's not the only method, but it's a good one.
As you can see, methods often go step by step. They're very orderly. First this, then that. When you're following a method, taking each step at a time, you're being methodical. You're doing things methodically.
For example, Hermione is a methodical student, and she studies methodically. Here's one of her methods for learning so well and achieving so much: she reads her textbooks before she goes to class.