It is a general fact of computing that after a while, the shiny, new computer that you've bought will start to slow down, especially after you've installed programs and anti-virus, and started storing files and media.
There are a lot of ways to improve the performance of Windows, and your PC, without having to upgrade anything.
The simplest thing to do is delete any programs that you don't use.
Go to programs and features on the control panel (if you are looking at the control panel in category view this will just be programs)

A list of the programs installed on your computer will appear. From here you can select to uninstall any programs that you don't use, or possibly don't recognise.

If you have no programs installed that you can bear to part with you can try limiting the programs that start when the computer starts.
Click start and type MSCONFIG in the search bar.

Under the startup tab you will see a list of all of the programs and applications that start when the computer boots.To disable all the programs click Disable all, to only disable selected programs just untick the box.

If this still doesn't work, you're going to have to start getting techinical.
First you can try defragmenting your disk. This means that any files for the same program stored in seperate locations on your hard disk will all be put in the same location. This means that the system will not have to spend as much time looking for the files in seperate locations.
To defragment the disk, go to my computer, right click on the disk you would like to defragment and select properties.

Under the tools tab select defragment now.

You may find that your PC is scheduled to defragment regularly. However, if you would like to bypass this and continue with the defragmentation then you can just click defragment disk.

You will then be able to see the progress of the defragmentation.

If you still don't see an improvement in performance you can try performing a disk cleanup. You can do this from the general tab of the disks properties.

The system will calculate how much space you will be able to free.

You can then select what you would like to delete from the disk.If you click on clean up system files the system will also check for any system files that are not needed, in order to free up more space.

When you have selected the files you would like to delete you will need to confirm your decision.

The system will then clean up the drive.

If this still has no effect (maybe now would be a good time to start thinking about an upgrade), you can try running less programs at once, for example only having one browser open, and closing any programs that are just sitting idly.
You can also adjust the visual settings for better performance. Open your control panel and in the search bar type "performance information and tools" and select the link that comes up.

You then need to select Adjust visual effects in the sidebar.

The best option is to select the option "Adjust for best performance"

The appearance will not be fantastically pretty after you click apply, but you may find your computer starting to perform a bit better.

If you'd like something a little less boxy you can choose to let Windows decide what is best for your computer.This should, in theory, balance prettiness and performance.
A simple tip for improving performance is to restart your computer regularly, at least once a week. By restarting you are forcing any processes and applications running in the background to stop running. Now you may think shutting down computers is something everyone does every day and so this should be fairly common sense, but if you're anything like me, laptops won't get restarted often. I just close the lid on my laptop and let it go to sleep!
Checking for viruses and spyware is also a good move, because your PC may be running slow because it has been infected.
If you've made it this far and your computer is still running slow, well the only remaining options are upgrades.
You can try installing more RAM in your computer. Windows 7 can generally run on 1GB of RAM, but it runs better with 2GB, and for optimal performance you could try running it with 3GB.
The other option is to check the speed of your computer, and decide if you need a new computer entirely.
To check the speed of your computer using the Windows Experience Index you need to open the control panel and search for performance information and tools. When you click the link you will see a score on the home page. If this number is lower than 2 or 3 it might be worth getting a new computer!

Looking at this score, I should probably consider a new computer at some point!