You need to be systematic but it depends to some extent on what state your computer is in. Assuming your computer is operating but not optimized, do tests in the following order:

Hard Disk

• Check Disk - The best way is by running the "Check Disk" program. In Windows XP there is more than one way to access it but the best is by using the Command prompt (DOS prompt). Go to Start>All Programs>Accessories>Command prompt. Type chkdsk /f. The space followed by /f requests Windows to fix any faults found. In Windows XP when you do this, it will say that it needs to run at start up - when it does this, choose y (=yes) and press enter. Next time you start your computer, Check Disk will run and look for any signs of disk failure.
• Cleanup - You probably have all kinds of junk on your computer's disk that is not needed. You can find and erase what you don't want by using the Windows Disk Cleanup Utility. Go to Start>All Programs> Accessories>System Tools>Disk Cleanup. After a minute or two, the program will list all files that you can safely delete. However, I don't like "compressing old files" so I leave that one unchecked. You might be surprised how many unneeded files you have. Once you have finished with this, you can select the second tab More Options and see if there is more space that you can free up. Two of these are discussed separately below (Unwanted Software and System Restore).
• DeFrag - It used to be said that you should do a DeFrag every week. However, with recent computers, a defrag is needed much less often - I do it about once a year. When a computer saves a file on a disk, it puts it in a semi-random location. In some case - especially large files - it needs to split the file into more than one location so the file becomes fragmented. Reading a file that is fragmented is slightly slower than a contiguous one. If your disk is close to full, fragmentation is a lot more likely. Doing a DeFrag is a slow process but worth doing occasionally. Before you start, turn off your screen saver and close any program you have running (e.g. e-mail) to stop the process being interrupted. To stop your screen saver, go to Start>Control Panel>Display>Screen saver (or Start>Control Panel>Appearance and Themes>Display>Screen Saver ) and in the drop down menu under Screen Saver, choose none. (When you are finished with the Defrag, go back and choose the screen saver previously selected.) Now go to Start>All Programs> Accessories>System Tools>Disk Defragmenter. Choose the disk you want to Defrag (e.g. C:) and select Defragment. It will first analyse and report - it may say you don't need to defrag in which case stop! The process could take an hour or two.

Security

• Updates - Your computer is not secure against damage by viruses unless Windows is updated. This is especially true with Windows XP but XP makes it easy to stay updated - especially if you have broadband internet access. Go to Start>Control panel>Security Center then ensure the Automatic Updates are on. If you then choose Manage Security Settings for Automatic Update, the easiest is to choose the top selection Automatic (recommended).
• Virus check: Even with updates, Viruses can get into your computer whenever you surf to a site that's not one of the major ones or whenever you receive e-mail from anyone. Or that CD that a friend gave you may include a virus. If you don't have an Anti-Virus program installed, get one - more on this subject here. If you want to know if you currently have a problem, on-line checks are available from several sites.
• Spyware Check. Spyware can be dangerous and also slow down your computer - make sure your computer is clean - more here.

Clean-up

• Unwanted Software - If you have had your computer a while, you will have software installed that you don't ever use. You should remove these programs. The easiest way is to go to Start>Control Panel>Add or Remove Programs. Then look down the list for anything you don't use. If you don't know what is is, leave it alone - you may need it but not know it! Then, one at a time, click unwanted ones and select Remove.
• Clean your Registry - The Registry is the central file that controls what happens on your computer. It can get quite big and can include errors and unwanted entries that slow your computer down. If you are not confident with this tune-up process, this is the step to skip. More on this subject and a link to a free "Cleaner".
• Virtual Memory (Page File) - All Windows versions use Virtual Memory. If your RAM is too small, Windows will use disk space instead - but of course disks are many times slower than RAM. If you don't have enough Virtual memory, the situation is worse - your computer will freeze or crash. Chances are the Virtual memory setting is OK, but to check, go to Start>Control Panel>System>Advanced> Performance>Settings> Advanced>Virtual Memory>Change (Or Start>Control Panel>Performance and Maintenance>System> Advanced> Performance>Settings> Advanced>Virtual Memory>Change) Then choose your main disk (C:) and select System Managed Size. If you want to "take charge", you can change the size of the virtual memory to 1.5 times your RAM size.
• System Restore - This applies to Windows XP. If you make a change to your computer and you now have a problem (e.g. you installed a new program, the computer behaves slow or badly and uninstall did not fix it), you can go back to where you were before with System Restore. To access the System Restore dialog, go to Start>All Programs>Accessories>System Tools>System Restore. (You can also get here via the Control Panel and System). To restore to an earlier time, select Restore my Computer to an earlier time. To configure Restore, select System Restore Settings. Then move the slider to select disk space. Mine is set for 5% which is 11000 MB (11GB) which is plenty. Depending on your disk size and available space, choose a suitable setting. If in doubt, leave it alone. You can also turn it off altogether here if you want (not advisable).
• Startup Check - When your computer starts, it also starts up programs. Most of these are wanted but some are not (e.g. I don't want AOL!). If you are not confident with this tune-up process, this is another step to skip. To find out which are starting, go to Start>Run and type msconfig in the box and click OK. Then select the Startup tab. If you see a program you know should not be there, unselect it. If in doubt, leave it alone.
• Unwanted Processes. To find out which processes are running in XP and Vista, you can press CTRL-ALT-DEL keys simultaneously and look at the list of processes under the Processes tab. But how do you know if a process is benign? Use Process Library to identify processes that don't belong (e.g. from a virus, or a program you thought you deleted). It does not help delete processes but helps tremendously in the detective work.

System Test via Internet
To find out if your computer has problems and to find out useful information on its configuration, use the OnLine test from PitStop. Go here for more detail.