I was going to write a long explanation of spyware and it's symptoms and causes however there are very good articles on other websites that have been written already.  Instead of re-inventing the wheel I'll directly quote and abridge these sources into one, compact but understandable article, while writing my own comments here and there..

FROM WIKIPEDIA (abridged):  Spyware is computer software that collects personal information about users without their informed consent. The term is often used interchangeably with adware and malware (software designed to infiltrate and damage a computer respectively).

Personal information is secretly recorded with a variety of techniques, including logging keystrokes, recording Internet browsing history, and scanning documents on the computer's hard disk. Purposes range from overtly criminal (theft of passwords and financial details) to the merely annoying (recording Internet search history for targeted advertising, while consuming computer resources). Spyware may collect different types of information. Some variants attempt to track the websites a user visits and then send this information to an advertising agency. More malicious variants attempt to intercept passwords or credit card numbers as a user enters them into a web form or other applications.

How can you get spyware?

• Downloading files and programs
• Of course not all downloads are bad.  Most of the time, malicious files are embedded in "free" downloads of programs, music, movies, etc. 
• Opening e–mail or instant messages
• Attachments are an easy way to install malware on a computer BUT you can become infected just by reading email in the "reading pane" of a program like Outlook.  This is why Outlook 2003 disables pictures and ActiveX controls that are embedded in emails that are shown in the reading pane by default. Most people just re-enable this feature, which can open them up to spyware and viruses.
• Visiting tainted Web sites
• In a similar way that just reading email in the reading pane of Outlook can infect your computer, visiting a webpage can also be risky.  Websites can automatically run scripts (small programs) when you visit.  Microsoft started to combat this by adding a yellow toolbar that will popup on a website that has a script that tries to run automatically when you visit.  The yellow toolbar popup doesn't mean that there is a malicious program trying to run, only that some type of script (usually an ActiveX control) is trying to run.  Only let this script run if you trust the website that you're on.
• Clicking on pop-up ads
• These popups can take you to tainted websites or directly install programs when you click on them.
• Sharing your computer
• This one is self-explanitory
• Just browsing the Internet
• See "visiting tainted websites" above.

How do you know if you're infected?

Once you have downloaded and installed the infected software you may notice that your computer starts running noticably slower, you have more "popups" and advertisements showing up on your computer, or that your computer starts crashing.

Another way is to purchase and install a program such as Webroot Spysweeper before you become infected.  This software is excellent at detecting and removing spyware.