Typically, the easiest way to tell you have spyware is because your PC is running at a reduced speed. The other way to check is to hit CTRL + ALT + DELETE and hit task manager (if you have windows service pack 2. If you have before SP2, then this should automatically bring up the task manager).
Once the task manager is open, check your running processes under the "Processes" tab. If you see a lot of strange processes running you do not recognize, you are probably infected with spyware, ad-ware or viruses.
An example of strange processes would be a fgkosk.exe or copies of the same process running twice. Some "smart" spyware can actually disguise itself as other windows processes – you can tell this if you have copies of processes running. Do not end task anything you're not sure of –ides, most of these files are actually able to resume themselves after you close them as they're in your windows registry.
You could also download a program that checks for these infected files, such as Avast, Ad-Aware, etc. Check my other article on "what to do once you have spyware" for a list of good programs to use.
The best way to get rid of spyware, ad-ware, or viruses once you have them is either to use a program made for doing exactly that. Failing that, you could format your PC. Sometimes, an infestation becomes so bad you may have problems downloading, installing, or running a program that can help. For more information, refer to my article on "What to do once you have spyware, ad-ware, or viruses."