There are several things you can do to increase the "speed" of your computer.
1) Clean up the disk. Uninstall unneeded programs (especially those that run at startup and/or put something in the system tray), run Disk Cleanup, and defragment the drive. This is a good first step that will almost always take a few seconds off boot time and application loads for any computer.
2) Stomp auto-starting programs. Click Start > Run and type "msconfig" at the prompt. Click the Startup tab and look at all that junk that loads when you launch your PC. Do you really need "Adobe Reader Speed Launch"? Probably not. Turn off anything else that looks useless, but be careful not to disable your anti-virus and important system components.
3) Run a full anti-virus and anti-spyware scan. I would recommend using AVG Free Anti-virus, Spybot - Search and Destroy spyware remover and Ad-aware spyware remover. These programs are all free.
4) Clean up the registry. CCleaner, available at http://www.ccleaner.com is free and worth running. It will also remove unused files from your system - allowing Windows to run faster and freeing up valuable hard disk space.
Those are the easy and free things you can do. If your computer is still slow you need to move on to the bigger guns.
1) Upgrade RAM. This is the one killer trick that will make almost any computer run faster. With an older PC, you will rarely have enough RAM to run today's memory-hogging operating systems and applications, and adding a high-capacity stick or two of quality RAM will give you a quick speed boost. Adding RAM is fairly simple, even for a novice, and you should be able to do the job in 5 or 10 minutes.You can run a free test at http://www.crucial.com and find out what kind of RAM (memory) your computer needs.
2) Reinstall Windows. If the above tricks haven't helped, it may be time to wipe the slate clean and start again, reformatting your hard drive, reinstalling your applications, and restoring your data files from a backup. You'd be surprised how much more responsive a freshly reinstalled Windows system can be, as you've wiped out years of temp files, garbled registry entries, old versions of software programs that have been upgraded repeatedly, and all sorts of other electronic junk. Reinstalling is easy if you have the "recovery disk" that came with your PC, and only a bit more involved if you're using a retail copy of Windows XP. Just be sure you back up everything you want to take with you before you pull the trigger!
3) Upgrade your hard drive. This is a more complicated solution, but if you're reinstalling Windows (per the prior tip) you might consider upgrading to a bigger and possibly faster hard drive, too. Hard disk storage is a performance bottleneck on every machine, and magnetic disks degrade over time. Some performance issues could be caused by a failing hard drive, even, and upgrading to a new model could really put some zip back in your system. As a bonus, you can use the original hard drive for backups or occasional storage, if you put it in an enclosure.