In reply to spinningholds:
What they said. Plus:
Slow down and do some people-watching.
Assuming you're more-or-less the same design of human as the rest of us, you'll need time between efforts for your fingers and/or lungs to recover. (Hang on as tight as you need to, not as tight as you possibly can. Climb like a t-rex using balance and the relatively vast muscles in your legs rather than your forearms... those two statements alone have got four hours of training value in them to unpack...)
Everyone else also needs time. They will be standing around too, encouraging their mates or shaking out or avoiding their spouse for ninety minutes or whatever.
Use the time to watch how others tackle the problem you were trying. Climbers are largely different shapes and sizes, so you can always learn something, even if what you learn is "I am too short/tall/inflexible/weak/clumsy footwork to use that approach."
Well your footwork can improve really fast. And if you are short, or tall, watch people who are like you but also the opposite from you, because you'll learn something useful in each case.
Use some social skills obviously. People can tell if you're leering. Watching for technique is totally legit, expected, nobody should be uncomfortable with it and explicitly acknowledging "thanks, that was cool to see, I'll try it that way now and see how I get on" or something can break some ice, ice which is most likely only on your side anyway.
Stick at it - go back to a route after trying something else. Trying similar standards or styles. If you can, going at roughly the same time of the week. Good things will happen. Someone will end up giggling with you at a spectacular fail - yours or theirs. Someone will give you clues. Sometimes that person will be a patronising show-off who you don't need around for more than a few minutes, but they may have nice friends, and/or they may turn into a lifelong climbing pal. If you stick at it you'll see the same folks and they'll see you and it gets more comfortable.
Chat to/nod at the staff at the desk. Not when they're busy or when they're trying to get their own stuff done. Ask them or look at the introductions board to find other lonely folks.
Climbing more than anything else I know of is a sport where people want you to succeed, and your success doesn't take away from theirs. Find a short one, a tall one, a weak one and an inflexible one to climb with so you can laugh at each other and help each other's weaknesses. It's a sport full of low social skills folk who don't mind grunting at you and ignoring you, but the other ones are keen to welcome and help you, just a bit shy to know how. Be welcome and find your way.
Y