Spyware is difficult to detect just solely by observation. While you may notice some sluggishness in your PC's performance, most spyware programs do not directly affect how the computer runs. You may notice an increase in the number of pop-up ads you see when you surf the web. You may also notice advertisements displaying on top of the normal banner ads you find on selected websites.
The best way to detect spyware is to use an anti-spyware program. These programs scan your computer for known spyware programs, alert you to their presence, and give you the option (if you choose) to delete the spyware from your system.