Mac viruses are so rare that it's hard to say. I've never encountered one in a decade. The main clues would be that applications stop working as they normally do (hard for a new Mac user to judge) and that overall processing, especially Internet access, slow down because extra (unauthorized) processing is going on.
The few security scares that got publicity in the past year were "proof of concept" programs that demonstrated a weakness in Mac OS X security, and Apple promptly closes those holes with easily-installed updates, for which you use the Software Update panel in System Preferences.
I think it wouldn't be much different than a PC virus. I wouldn't worry too much about getting a Mac virus. I would say you might want to get a virus scanner anyways. Why? Because if you get an attachment from a PC user and its infected with a virus, and you can unknownly send it out again to another PC user, giving that person the virus. Yeah, not a great way to make friends. Same goes for spyware, don't have to worry too much about it. I'm sure it will be all over the news when the first one that is a real virus or spyware comes out for the Mac.