Although Spybot may have given you a list of the spyware it found, you shouldn't just jump straight in and remove it. Some spyware masquerades as a different type of spyware, and incorrect detection doesn't result in correct removal. The mantra for this stage is search, search, search again, and search a little bit more to be sure.
An hour spent searching at this point can save hours of frustration and problems later. There are too many types of spyware and malware that will actively try to damage your system if removed incorrectly, so make sure you know what you're dealing with.

With automated tools such as Spybot and HijackThis, removal of spyware is generally as simple as selecting the Fix option. There's one piece of spyware that does merit a special mention due to its nastiness: CWS.
Variants of this malware integrate deep inside Windows, making removal very difficult. If you're unfortunate enough to be infected by this menace, a great tool called CoolWebShredder can generally fix the problems.

There are a lot of antispyware tools that can help with removal and cleaning. If you'd like to learn more about different products and what they can do for you, CNET's Stop direct marketers from spying on you is the place to start.