Tonight my computer detected a trojan/virus that seemed to do a couple of weird things to my computer including turning off my firewall and disabling my system restore function. Whenever my computer had a trojan/virus before, I would just do a system restore and everything would be OK, but tonight everytime I tried, it told me that it couldn't do it because no changes had taken place since that restore point or something to that effect.

After rebooting, Avast did a complete scan, deleting a number of trojan files, including some in the system restore program. When ther first trojan files were found it asked me what I wanted to do with them and I selected "delete." After that, it automatically deleted any trojan files it found. The scanning seemed like it was going to take a while so I left the computer and went off and did something else. When I came back, the Avast program had exited automatically so I assumed that it was finished. There was some type of log in the Avast program folder but I couldn't really make much sense out of it.

Also, now that the trojan files have been removed, should I try to do a system restore to make sure that it's working properly or should I just leave everything alone since my computer seems to be back to normal?

I'd recommend looking up a free HijackThis analysis site/forum and have a malware removal expert help you as in most cases it may take certain removal software to fully remove the infection.

It hasn't returned as of today - so far so good...

You're saying "Whenever my computer had a trojan/virus before", which makes it seem like that happens quite often. You should ask yourself what it is that you're doing - (opening random attachments, downloading programs or "codecs" from suspicious sites, etc.?) or not doing (automatic updates turned off, using the unsafe Internet Explorer, etc.?) - that allows your PC to become infected by viruses or malware.

Lack of awareness about certain pitfalls is really what gets PCs infected. Maybe you should take a look at something like this: http://www.cert.org/tech_tips/home_networks.html