Tips for gymtimidation?

What debubbie said. Trust me; they don't really care that you're a beginner. They might take notice if you're obviously not putting in any effort -- lounging on the equipment, for example, using lazy form, or chitchatting incessantly in a group class. IME though, people are generally understanding toward beginners. Experienced gym folks are usually pretty nice.

Short of bad gym etiquette that disturbs other people's workouts... nobody cares what other people are doing. I think most of us who got out of shape had some of those feelings at one point. But it doesn't continue. People take no notice of you and you build confidence. It took me awhile to do anything but cardio, then to move from machines to free weights. Do whatever you feel comfy with.

Echoing what others have said, there isn't a reason to worry since everyone there is just trying to get their own workouts done and have their own insecurities as well. We all started out awkward at first but after a couple weeks you'll probably fit right in and become much more comfortable. You might even make a few friends.

Even if they are judging you in a really obvious way, it doesn't matter - a) if they're like that, they're jerks, so who cares; b) ok, say you do care - that jerk's judgement will only last for 5 nanoseconds, and they'll go back to admiring themselves or whatever they were doing - you only exist for 5 nanoseconds, to them; c) you paid your fees, the same as they did, you've got a right to be there; d) your muscles still need the workout.

If there is an uncomfortable moment, just take a breath and shut your eyes and think about your form, and the muscle groups you're working exactly at that second. Shut them out.

99% of people are either cool or don't care, I'm just saying that in case you run into some obnoxious teenagers or something.

As someone above said, there is basic gym etiquette that it might be helpful to know, though, to smooth interactions. I recently had a moment where I used what I thought was an unattended cable machine. Apparently a guy (who was nowhere in sight!) had been using that machine as well as another (across the room) for a superset or something. He glared at me as I finished my set, that was awkward. But that's on him, as far as I'm concerned, because usually, when people do that, they leave a water bottle or jacket or something on the machine to signal it's in use. Or they let you know if they're using a piece of equipment and are just on a rest. (You could also ask in that case, i.e. if someone's kind of hanging around something you want to use - just say, "are you using this machine, do you mind if I work in" - usually they'll let you). That's about it. Oh, and wipe equipment down after you use it, and don't show up with a hacking cough or seeping wound. If you have those things covered, forget about everyone and just do what you went there to do.

I guess I'm just too old to be intimidated. Nothing anybody else is doing matters to me at all. Fake it til you make it. Walk in there like you own the place and you don't give a crap what anybody else thinks. The more you practice confidence, the more real confidence will build naturally in you over time.