It depends what you’re trying to do. You can either make things static, or you can create an instance:
MainClass instance = new MainClass();
btn.Clicked += instance.StartClick;
btn_stop.Clicked += instance.StopClick;
I assume this isn’t your real application, so it’s hard to say what you should do in your real code. Personally I’d lean towards creating an instance – static variables represent global state which is usually a bad idea (in terms of testability etc). We can’t tell whether that affects your situation or not though.
What’s important is that you understand why you’re getting the error message and why the above change fixes it. Once you understand that, you’ll be in a better situation to make the best decisions.