How do I retrieve data from my broken computer?

So I dropped my laptop and now it won't work. The Geek Squad guy said my motherboard was probably broken or something of that nature. He did say that if I were to get a new laptop, he would be able to retrieve the data from my old one and put it onto the new one. I was wondering if anybody knew how I could do that on my own without having to go through the wonderfully fabulous Geek Squad.