What do I need to know about wireless security at airports or hotels?

So...I just got a new Asus computer, a tiny 700 series wireless notebook. I know zilch about protecting my computer when traveling, but installed Avast for antivirus protection. Whatever I do, it has to be a small program, as the Asus doesn't have a lot of free memory. I installed Firefox and Open Office and Avast. It still runs..not quickly, but it runs. Maybe I already have some security running...WEP or something, but I don't know how to find out if I do or I don't. How can I check, and what else should I do?