If your computer has but 1 or 2 gigs of RAM, purchasing more may well help with performance, but otherwise will not. If you have a 32 bit version of Windows, the most you can use is about 3.5 gigs. You can see which version you have by right-clicking on Computer and choosing properties. On this screen it will tell you which version of Windows you have and whether it is 32 bit or 64 bit.
Things you can do to speed up your computer assuming it used to be faster than it is now.
1) defragment your hard drive
2) remove software you don't need, particularly software which starts when the computer boots.
3) remove any spyware/adware. Spybot Search & Destroy and AdAware are the two best free options there.
4) Check your computer for viruses. Make sure you have a current AV program installed with the latest definitions and run a full scan at the deepest level.
5) Go to blackviper.com and go through his configuration guides for whichever version of Windows you have. You will have to read through the recommendations and choose which ones to implement and which not to based upon your needs and usage.
If none of those things help and it is still slower than it was originally, back up your personal data/files and then perform a factory restore. This will return it to the performance it had when it was new, but it will not get faster nor can you make it faster.