It helps to know your computer. If you don't, do your research first. Some laptops have the LCD glued (epoxied) into the frame. In these cases it's usually much easier to replace the whole cover. Most don't have this problem though.
I'm going to show how easy it is with an Apple iBook G4. I've also replaced the screens on Panasonic, Gateway and other laptops just as easily.
Step 1: Gather Supplies
The later can be a couple of small (tiny) flat edged screwdrivers, a metal ruler or paint scraper with the edge filed to a sharper edge, etc. In my case, I use the tools that were included with a battery replacement for an iPod. The tools alone were worth the cost of the battery!
For some, a pair of tweezers would help.