Provided you can access the old laptop HD, remove it. Get your hands on an adapter for 2.5 to 3.5 HD connection. These are common, check http://www.newegg.com or http://www.geeks.com or any other online/local source. They aren't that expensive. You do have a typical 2.5HD right.
Once attached, you can treat your 2.5HD(w/adapter) as a std. IDE drive set to slave. Make sure you can set the old 2.5HD as slave(visit thier support website). On desktop mount it or leave attached by IDE cable to then swap files.
I have an old notebook hard drive which has some files that I want to remove. The old notebook is shot so I can't pull them off through it. How can I hook up the hard drive to a normal desktop?