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.
One of the most important methods you'll ever learn about is the scientific method. That's the step-by-step way in which we figure out what's true or how reality works.
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.