Before you do anything else, however, check if your warranty has run out. If it hasn't, stop reading this, and take your Xbox down to the Microsoft Certified Repair Center that's local to you and let them deal with it. You do not want to be looking for Xbox 360 repair guides if your warranty is still valid.
If your warranty has expired, then you need a course of action to follow. For those with limited time to solve these problems for themselves, then the quickest and best value for money option is to read Xbox repair guide reviews, and follow the advice, often written by technicians, that will get your Xbox up and running in two hours or less.
If you are interested in trying to ascertain what the problem is first, then you need to try and understand the Xbox 360 error codes first, which will start to give you a clue as to what you need to do. It is this error code system which is the Xbox's way of telling you what is wrong with it.