What you could try is making sure that only the programs you need are running in the background. These will chew up memory making your pc slower. You can choose which programs to have running when the computer starts by doing this;
> Click Start
> Click Run
> Type ' MSCONFIG '
> Click the 'Startup' tab
> Only uncheck the items which you know are programs you don't need (obvious ones). If you don't know what it is, don't disable it without consulting this; http://www.bleepingcomputer.com/startups/
> Click Apply then OK
> Next time your computer starts, it will display a message
> Put a tick in the box 'dont start ms config when windows starts' then click OK
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Next thing you should do is get Firefox. It's a safer, faster and more customizable alternative to Internet Explorer. Basically, when you get it, you will notice a big difference in speed. But bear in mind the fact that ISP's only ever gaurantee 'up to xxMbps'. You will be lucky if you get half that most of the time.
http://www.mozilla-europe.org/en/firefox/
(DO NOT download this from any third-party sites - only get it from the Mozilla site (link above)
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To improve the short term speed in IE, try clearing out it's temp folder, cookies and all the other junk it stores.
> When in IE, click 'Tools'
> Click 'Delete browsing history'
> Click 'Clear all'
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Download, install and run Ccleaner and also defragment your hardrive with Defraggler.
http://www.filehippo.com/download_ccleaner/
Download Defraggler - a better alternative to the built-in Windows defragmenting utility.
http://www.filehippo.com/download_defraggler/
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But if you have money to spare, upgrading your RAM would be a good start. It's not too expensive (I was offered 2GB for £20). Depending on your operating system I would suggest these amounts as the minimums;
Windows XP - 1GB (programs are getting more and more complex these days so this would put your pc at a good level to cope with newer software)
Windows Vista - 3GB (Vista itself eats up memory like nothing else, so if you want to run things on Vista at a decent speed you need lots of memory)
One of the best ways to find out what RAM is compatible with your computer is to run the online scanner from Crucial (one of the biggest memory manufacturers):
http://www.crucial.com/systemscanner/index.aspx
(you will need to use IE for this)
You can also find out how to install RAM by watching the videos below (you can do it yourself - it's easy).
Desktop: http://uk.youtube.com/watch?v=r2EC4BxtBSY
Laptop: http://uk.youtube.com/watch?v=yirNejnzbEM