So, to start, go ahead and power off your laptop and take out the battery so you're free to work on it without any worries. If you have all sorts of junk on yours, like I had on mine, you can scrape it off and use a little adhesive remover to get it nice and clean again.
Now, unroll your contact paper, and lay your computer on top with the grain going wichever way you want, then cut around it, leaving a large boreder on all sides (you'll trim it down later).
Now, you can decide what you'd like to do about the logo on your cover. I decided I wanted mine to outline it, so I used a piece of tracing paper to trace the outline, then laid it over the contact paper in the middle, and cut out using a x-acto knife (I used a little piece of tape to keep it in place while I cut it out). You could also just cut a large round window for it and use a bottle cap or anything that's nice and round.
After you cafefully remove the backing, lay it gently on top of your laptop, careful to line-up where your logo cut-out is, and smooth the contact paper out. Then, flip over so the top of your laptop is now on the floor, and begin trimming the edges. I used my straight-edge ruler and "eyed" it the best I could, re-trimming it if I needed to. Then you just fold up around the edges of your laptop.
If you don't have a round edge laptop, or just don't want your cover to "bleed over" you can also just take the measurements of the area that you want to cover and cut it out before you apply it. And if you'd like your corners rounded a scrapbooking photo-round cutter would work perfect!
I also decided to do the inside too since it was pretty beat-up looking as well - I used pretty much the same type of process to do the inside that I used on the outside, tracing the trackpad and cutting it out beforehand to get the right size.
