First thing to know is: you won't make a fool out of yourself. There is nothing
"foolish" about being new to a gym or new to the equipment/weights in a gym. Seriously, it is totally normal NOT to know how to properly use all the stuff in a gym. And trust me when I say that half the people in there -- even the ones who LOOK like they are doing it "right" -- are probably doing it wrong. Do you know why? Because they are too embarrassed to ask questions. Don't let that be you!
If I were you, I'd call the fitness center and tell them you are a new client and would like someone (a trainer) to take you through the facility and explain the proper way to use the equipment. When you get the tour, ask lots of questions and make sure you're comfortable with the stuff that looks interesting and fun to you.
I don't know what your exercise goals are, so it is hard to recommend what you should do. If you are knew to the whole thing, maybe you'd like starting out on the treadmill/bike/stair climbers.