When you first purchase a computer, even after the first few programs are installed it remains blazingly fast! However after a few years of use your computer operation will slow down - imagine a partial blockage in a hosepipe that cannot be seen. It's such a gradual process that you hardly notice, but the more you use that hosepipe the more blocked it will get. This analogy could be taken further and you might consider the hosepipe's connection to water which is not clean an added cause for blockage (= pirate programs? / viruses / adware etc) or leaving the hosepipe outside for ages and not being wound up (= no maintenance / housekeeping), but as I don't do analogies...

So here are the top 8 ways to counteract everything that slows down a computer for FREE! Applicable to Windows XP or windows Vista, ignore this if you don't know what it means.

Defragment Your Hard Drive(s)

If you don't do this your hard disk(s) become fragmented by general use and when you new programmes are installed. When you install a program the file is generally placed on one part of the computer but after a while bits and pieces of data are spread across the hard disk. By using Windows 'Disk Defragmenter' the software moves all the bits of data into roughly one place. You can get to the file by clicking:

Start
All Programs
Accessories
Disk Defragmenter
Once the programme has fully loaded click on the top drive and work your way down.

Disk Cleanup

Disk cleanup performs 'housekeeping'. When you load most programmes, often bits of data that may have been used while the programme was running are left behind. Those programs don't generally bother deleting those, which can slow the computer down. You can easily and safely delete those bits of data by clicking:

Start
All Programs
Accessories
Disk Cleanup
If it comes up with a list of boxes make sure all are ticked.

Uninstall Unused Software

Uninstalling unused software speeds up the computer by freeing up space on the hard drive, cutting down on all the 'data sludge' that it has to wade through for normal use. To do this click the following:

Start
control Panel
Add or Remove Programs
Scroll threw the list and find the programs that you wish to remove
Click 'Add/Remove' or 'Remove'
If it asks you to confirm removal click 'Yes' or 'Confirm'

Run Windows Update

Windows update is a update service offered by Windows (surprise surprise). The updates
are generally security related but they can also include patches for added
stability. To run the update simply click:

Windows Update
And then complete the following
Windows XP
Start
Control Panel
Automatic Updates
Check the circle next to 'Automatic (recommended)'
Windows Vista
Start
Control Panel
On the left is 'Change Settings'
Check 'Automatic (recommended)'

Disable Indexing Services

Windows Indexing Services is a service that categorises all the files and folders on your hard drives. The problem with this is that it also slows down the computer considerably. To disable it click the following:

My Computer
Right Click 'Local Disk (C:)'
Click Properties
Uncheck 'Allow Indexing Service'

Stop Unwanted Start-up Programs

When you start up the computer and other programs automatically start that you don't necessary want at that time. Another problem is that it also slows the computer down. To remove the programs from start up (this does not remove the programs permanently) click:
XP - C:\Documents and Settings\All Users\Start Menu\Programs\Startup
Vista - C:\ProgramData\Microsoft\Windows\Start Menu\Programs\Startup

(Note - this directory is hidden by default)Delete the programs you don't want in loading when the computer starts up.

Extra Ram

RAM stands for Random Access Memory and your RAM helps to process all the information that goes through the computer. Broadly speaking the more RAM you have, the faster your computer. Unfortunately it does cost but prices are relatively cheap.
I use a website called 'Crucial' and they have a nifty little tool to help you sort things out.

Crucial - Homepage
Crucial System Scanner
Error-Checking
Error Checking can help diagnose and even correct a wide range of hard drive errors. It helps stability, speed and may even fix a few errors. To do it click:
Open 'My Computer'
Right click on one of the Hard Drives (usually C:)
Click 'Properties'
Click the 'Tools' Tab
Click 'Check Now'
Click both the boxes
Click Start
Restart thee computer if asked.

Notes:

You may want to bookmark this page for future reference, Firefox: press Ctrl-d to bookmark or 'Bookmark this page' in 'Bookmarks'. Internet Explorer: Press Ctrl-D or 'Add to Favourites' in 'Favourites'. Before we continue it is highly recommended that you back up your computer.
I cannot be held responsible for any problems that may be incurred while carrying out these suggested actions, however I may offer remote diagnostic assistance to help fix any existing computer problems.

I recommend you do this twice in a row and then repeat once a month. Hopefully after that your computer should be blazingly fast. If not, or if you want more speed try the links below. Also I don't recommend that you use any software apart from the software that comes with Windows.