AdAware works just like SpyBot.
Avast is like any other anti-virus, it does active protection and you can scan with it.
To do a full scan with Avast, right click on the 'a' icon on your toolbar and choose 'Start avast! Antivirus'. It'll start up and scan all of your running programs. When it opens, click on the top icon on the right side (local disks), then set the type of scan you want to use (do thorough the first time), and press the 'play' button all the way on the left.
...then wait while it scans your hundreds of thousands of files.

(I'm close to 500,000 files now.

)
It always asks for confirmation to delete/quarantine a virus for me, I've never checked if you could make it do that on its own. So, you might wanna do it when you can be around to check on it once in a while.