So, my grandma was being very generous and decided to buy me a new laptop. I had told her to get me at least a pentium, and at most a dual core (after that I wasn't very picky [besides hd and memory]). Well AFTER she had already paid for the laptop I get to find out that it is a Celeron R 900 @ 2.20 GHz, 2.19 GHz Toshiba with 2 gigs of ram.

What can I do to make this darned computer better/faster/not freeze up when I play simple games?
I've thought of getting an external hard drive and more memory, but I don't know if either of those will make a real difference in the performance.

Any help?

Trade it in while it is new. Deliver papers to earn enough for the change over.

An external HDD would be useful but not have an effect on performance, more Ram will help, but your issue is probably from the Graphics processor.
Tell us what kind of GPU you have/what games you're playing. You may have to do what Kcircyrd suggested