Oh Stephanie, you poor thing. I SO know what this feels like. I wish I could be there to help you through this first time. Because I just so know what that's like. But let me tell you, as scared as you may feel is just how freakin awesome you are going to feel once you make this your own.
I get this anxiety EVERY SINGLE TIME I try a new lift. I've been working out at the same gym for five years and it does get a little easier. Now, I pretty much feel confident to do whatever I please because I have "proven" myself. But that first time, and yep, it is male dominated. But ya know what...once you do it successfully you totally own the floor.
K. Here's my advice.
First, have you done a back squat with a free bar on your back before? If not, I would only use a dowel, or practice with a broom handle at home. Get that form down pat. I'll provide you with some links to study so you can critique your own form best as possible.
Once you feel pretty good about going down and pushing back up through the heels and keeping that chest nice and broad then try it at the gym. I would first use a free bar (an Olympic barbell without any weights attached) That thing alone is 45 pounds and really is enough for the first time. Could you squat more weight. Maybe. But you need to teach your body the proper mechanics first.
Some gyms will also have a lighter weighted free bar, like about 35 pounds. See if you can find one. It will feel significantly lighter when you pick it up.
Here's another secret.

Most of those men don't squat correctly anyways. I've watched. Nope, they sure don't. A squat is a beautiful thing, when it's done successfully. When done incorrectly it can make me wince the same as nails on blackboard. And just because they are male they do not intuitively squat better.
Watch the videos, Check out the book Starting Strength from the library by Mark Rippetoe, and check out
www.Stumpteous.com for tips as well. Practice at home to feel somewhat confident in your movement and then try it with a free bar.
Something else that I recall during my early squatting sessions, there is a point in which adding more weight made the squat movement "feel better" It's difficult to describe but for me, if it's too light my form gets a little sloppy unless I've already squatted heavier in the session or did proper activation movements prior to the squat.

It's kind of like a little extra weight forces me to "sink into the correct form and think" about the movement. Anyway, you'll have your own experiences as well. I'm rambling here. Just take a deep breathe, walk on over there and claim your bar.
Oh, and it wouldn't hurt to get a trainer to help you either. I did.
http://www.youtube.com/watch?v=kawBY5p29fQ
http://www.youtube.com/watch?v=kawBY5p29fQ
http://www.youtube.com/watch?v=yha2X...eature=channel
http://www.youtube.com/watch?v=Rq8CW...eature=related
http://www.stumptuous.com/