The best way to speed up your computer is by adding more RAM(Memory). I recommend at the minimum 512MB of RAM. Having this much will ensure that your computer will stay running smoothly. There was a lot of Windows XP computers that shipped out with 128MB and 256MB of RAM. With all the Windows Updates and and new antivirus and security suites, having 128MB or 256MB is not sufficient anymore. Installing RAM in the computer is easy, it only installs one way in only one kind of slot on the motherboard. I recommend Kingston Memory or Corsair as they are pretty reliable brands of RAM modules.
Another trick you can try is in Windows. Follow these steps to make your Windows experience a little better
1. Click Start
2. Right-Click My Computer, then Properties
3. Select the Advanced tab
4. Under Performance, select Settings
5. Select Adjust For Best Performance