Ok, heres what you could do:
1) Upgrade Your Processing Chip (most expensive choice, probably better to just buy a better computer, follow what Indi said so you can get the best you can).
2) Upgrade Your Ram (Will increase the amout of memory your computer has to store information. The more memory, the less variable swapping, the less time it takes to store things that need to be accesed often).
3) Upgrade Your Video Card (A new card that costs around $100 will increase the graphics processing speed quite a bit! Though you wont be able to process the new games, you will notice a speed increase, I'd suggest the new NVidia or Radeon cards).
4) Buy New Computer (You can buy a pretty decent one for probably less than $400. I'd say a P4 1.6 Ghrz 512MB Ram, and an Intel Graphics Video Card that you could easily swap out for another $100)
I would personally suggest doing suggestion 4. More bang for your buck, trust me.
@Transworld Punk 69: Yeah, overclocking increases the processors speed, but usually never twice its speed (or else we'd be seeing 6 Ghrz P4's everywhre). Chances are you could just get a better cooling fan, and you'll get some what of a speed increase. But, I wouldnt suggest overclocking, shortens the life of the processor if I'm correct.
Cheers,
Preston
Intel Celeron 1.3 Ghrz 512MB Ram NVIDIA GeForceFX 5200 128MB