Well, there should definitely be space for more RAM. I’d be very surprised if a desktop computer had fewer than 4 RAM slots, and your 1Gb is probably installed as 2x512Mb, leaving you 2 empty slots.
If you want to check for available slots without opening the case, go to the Crucial website and run their system scanner. It’s perfectly safe, and when it’s done it will give you a report telling you how much RAM you have, what type of RAM it is, and how many empty slots you have.
You can buy your RAM from Dell, but i had a look and their options seem rather overpriced. You can buy it direct from Crucial (good RAM, decent prices), or you can find it yourself elsewhere. For hardware online, you can’t do much better than NewEgg.
I had a look on Dell’s website for your type of computer, and i think that this Corsair RAM should work fine in your computer. It’s really cheap, and Corsair Value Select had a decent reputation, even if it’s not top-of-the-line memory. This Kingston value ram should also do the trick. (BTW, don’t trust my research; use the Corsair scan to check exactly what type of memory you need).
Each of those options is a 1Gb (2 x 512Mb) pack. Most people seem to think that 2Gb total is the required amount for running Vista, although some folks use less. If you want more, go for a 2gb (2 x 1Gb) pack. It will be more expensive, obviously, but you’ll probably get better performance, especially if you’re running multiple apps at once.
As for installation, i think you’d be crazy to pay for it. As long as you’re careful, installing RAM really is a piece of piss. The modules fit right into the slots with a firm push. The main thing is to be careful not to bash anything else, and also to make sure you ground yourself before poking around inside your computer, so that you don’t fry it with static electricity. Here is a set of decent instructions.
ETA:
If your games appear to be running slowly, it might not be RAM. If they are new, graphics-intensive games, the bottleneck might be in your graphics card. You didn’t say what graphics cards you’re using.