Remember that people are much more self conscious about themselves - including other people at the gym. People might look around, but at the end of the day we're all more worried about what we do, how we look, etc. We're all our worst critic!
It took me a loooooonnngg time to work up the courage to try some classes like Zumba at the gym, because I'm terribly uncoordinated and cannot dance to save my life. I thought I would look like a fool.
Now, maybe I still look like a fool! But who cares. I focus on the instructor, and myself. That's it. Everybody's too busy trying to get their own self in order.
Just don't have cellphone conversations at the gym (unless you're in the lobby or something), and we'll be cool!