Primary Rule: Common Sense! REMEMBER, Technology can do very less to stop you from smashing your own PC with a hammer. The ONLY best defense against any malicious technology is personal intelligence.

So, how do I know if someone spying my PC?
Here is Symantec Online security scan & virus detection. Follow the instructions. Those online tools will help you check your PC for possible threats. Symantec Security Check tests your exposure to a wide range of online threats. It's free and efficient, and it helps you determine your Internet security needs. Link: http://security.symantec.com/sscv6/

ZoneAlarm Spyware Scanner: Free online scan instantly finds spyware, keyloggers, cookies, adware, browser help objects and other pests, at no cost to you Get the option to remove spyware and download ZoneAlarm after the scan is complete. 
Link: http://www.zonelabs.com/store/content/promotions/spywarescanner/index.jsp

Are you getting a file/attachment in your email or removal media form a un trusted source?

Opening such files without scanning it with a proper antivirus scanner would be stupidity. All it takes for your PC to get hacked or infected by a malicious program is your double-click on that file. Even worst... sometimes, such malicious programs can automatically start without knowledge!  REMEMBER; your antivirus can't detect all viruses. If you are not expecting the attachment, why open it? BUT if you think* it has something important... you could send those files to a ONLINE antivirus scanner to look anything suspicious before running it.

Try... (Recommended) :

www.virustotal.com
http://sandbox.norman.no/live_4.html
http://virusscan.jotti.org/ 

Other online antivirus scan engines...
http://www.bitedefender.com/scan/license.php
http://www.pandasoft.com/activescan/activescan-com.asp
http://www.ravantivirus.com/scan
http://housecall.trendmicro.com

So how do I protect my PC? :

You got a Antivirus Software?

Go, get a free copy of AVG Antivirus for home use at: http://www.grisoft.com/

What about a Firewall?

Download a free copy of Zone Alarm. It provides solid protection against worms, and extreme protection against the latest hacking, spying, and identity theft tools.

Link : http://www.zonelabs.com

 ...and Spyware scanners?

Ad-Aware is designed to provide advanced protection from known Data-mining, aggressive advertising, selected traditional Trojans, Dialers, Malware, Browser hijackers, and tracking components. With the release of Ad-Aware SE Personal edition, Lavasoft takes the fight against Spyware to the next level.
Link: http://www.lavasoftusa.com/software/adaware/

Microsoft Windows AntiSpyware (Beta) is a new security technology that helps to protect your computer from spy ware and other unwanted software. You can manually scan your computer for spy ware or schedule the program to perform a scan automatically on a regular basis at any time.

Read the following articles to learn how to install and use this tool.
http://www.microsoft.com/athome/security/spyware/software/default.mspx

Virus removal tools:
Viruses have become increasingly complex and infections involve more system elements than ever before. Symantec Security Response has developed tools to automatically conduct what would often amount to extensive and tedious manual removal tasks. If your system has become infected, the tools listed below should aid you in repairing the damage.

Link: http://securityresponse.symantec.com/avcenter/tools.list.html