Carving watermelons is a lot of fun, and people seem impressed, since you don't see it as often as pumpkins. For the most part, the process is very similar to carving pumpkins. But here are some watermelon specific tips.
Grab yourself a watermelon that is big enough to fit the pattern you want to use. With a long kitchen knife, cut an inch or two off one end. This will give you access to the melon insides. It will also provide a flat base for the melon lantern to stand on when you're done. So make this slice nice and straight, so you'll have a flat bottom.
Scooping out the insides of the melon is the step where the process differs most from pumpkin carving. Unlike pumpkins which are somewhat hollow to begin with, you'll have a lot of juicy red flesh to remove from the shell. Have a very large bowl or pot nearby to drop the melon into. Not only will you have a cool melon lantern when you're done, but you'll have a ton of melon you can eat.
I use one of these tools to scoop out the insides of my watermelon. An ice cream scoop, a Monster Scoop
(top right) or a Jack-o'-Ripper Scraper Scoop
You'll loosen up a lot of juice as you scoop out the melon. They are called watermelons for a good reason. Make sure you keep the cut end upright while scooping, so you're not pouring liquid onto the floor. Every so often you'll want to dump out the excess juice (into the bowl or sink) so you can see what you're doing. Once you get most of the flesh out, you can also use a spoon or pumpkin scoop to scrape away the rest of the insides. You'll know you're done when the pink stuff is mostly gone and you can see the light green/white rind. Watermelon rinds are pretty thin to begin with, so once you remove most of the red stuff you don't need to worry about thinning the walls.
From there, the process is the same as carving pumpkins, as far as transferring the pattern and doing the carving. Some say the carving process is actually easier, since the melon rind is thinner than a pumpkin's. So you can cut clean accurate lines, even with complex designs.