it would be more helpful if you gave us some specs. Which operating system are you running? 98/Vista/7 ? Make sure your OS is up to date with Microsoft update. You can do this by -> start -> programs -> Windows update or google "windows update" and go to that website.
You said you have an anti-virus program. Make sure you have this updated also. If it isn't a full copy, I suggest using AVG anti-virus- free edition. Works great and saves you some money.
Spybot Search and Destroy is great. Just make sure it is updated and it should do the job itself.
Which Browser do you use? I suggest using FireFox - deleting your cookies and history can also help with speed. I have my browser setup to delete everything I do once the window is closed.
If your computer still not running faster, I would suggest a reboot. There are a couple ways to do this- the easiest would be going to start-> program-> accesories ->system tools -> system restore. I think most computers have a "restore to factory default settings" option. Make sure you save anything you want on a jump drive, or zip it and email it to yourself- because it will delete everything. If this isn't an option, see if you have any of the discs that came with the computer. There will be a recovery disc.
Hope this was helpful!