I'm going to assume they were demonstrating WEP cracking which is an incredibly weak encryption mechanism and you can usually crack a WEP protected access point in a matter of minutes. The tools are freely available to allow script kiddies to attempt this, look up the aircrack-ng suite if you're particularly interested.
The answer is simple, use WPA2 and a strong password containing uppercase and lowercase alphanumeric characters and symbols to prevent brute force attempts. As far as I'm aware WPA2 still hasn't been cracked successfully in small timeframes, and the research and tools aren't freely available yet to allow the general public to attempt it.
Another thing you can do (although this is security through obscurity) is to disable beacons on your wireless access point, it's pointless against anyone who has some knowledge on the subject and can easily be detected by something like aircrack but may keep the less technically aware at bay.
As for detecting whether someone else is on your network a lot of routers have diagnostic controls to allow you to see the clients currently connected via your router. Check your router control panel under diagnostics.
What should be more worrying is the potential for MITM (Man in the Middle Attacks) essentially allowing someone to ARP poison you and intercept all traffic between you and any other device on your network (i.e. your router). This would allow a third party to steal any sensitive data, for example bank details as you enter them. SSL certificates in this case can also be intercepted. You can easily leave tools running that will log all the interesting data and leave you none the wiser.