Here's some tips that might help.
Don't get caught up with judgement. I know it can be intimidating when you start going to the gym: You think that people will look at you and think you're an idiot because you're not doing an exercise correctly. Or they'll laugh because you're not lifting that much weight. Or they'll cringe because you have some belly fat. Here's the thing, people don't care. They just want to do their own thing and leave. They probably don't even notice you. Most people in there feel the same way you do because they think that you're judging them.
Don't judge others either. That gym bro in the muscle top with big jug of water who's flexing in the mirror...is none of your business. He's just doing his thing. Maybe it's not your thing but if he's not bothering you, don't hate on him. Same goes for the fit chick in the sports bra who never smiles; she's not a stuck up, full-of-herself bitch; she's just living her life and exercising the way she wants. Maybe she used to be ashamed of her body and now finally has the confidence to wear what's comfortable. We're all guilty of judging others but focus on yourself and why you're there. Assume people are nice: this all goes on in our heads anyway so we might as well.
Have a plan of action. If you know exactly what you need to do when you get to the gym, you'll feel more confident. If you're wandering around aimlessly, as well as not getting a decent workout, you'll likely start to feel self conscious. Have a set program written down so you can follow it and stay focused.
Ask a trainer for help. Don't be embarrassed because you don't know everything already. I don't know everything and I've been working out for 20 years and I've been a trainer for 8. We're glad to help. Confucius said “The man who asks a question is a fool for a minute, the man who does not ask is a fool for life.”