@wrestlos Start by smiling at her and see if she smiles back at you. Do this a few times. After that (if she smiles back) you can just say hi when you see her and see how she reacts. If she seems happy about it and starts saying hi to you, too, you can introduce yourself or ask her for her name and start small talk. Then you do this for a few times and then after you get to know her a little, you can ask her out for a drink.
A guy at my gym approached me (woman) like this and I really liked the way it went. It made me feel safe, I never thought that the guy was pushy or a creep and just felt comfortable. It will take time but that's much better than just asking you crush for her number, getting rejected and then having to switch gym etc.
And to add: as a woman I would say it's definitely fine if you approach a woman at the gym as long as you do it respectfully and back off if a woman tells you she's not interested. Just be polite and friendly and respect her boundaries. Yes, there's this stigma that women don't want to be approached and that you should leave them alone etc. BUT I would say that's heavily influenced by the fact that some creepy guys can't take no for an answer and are super unpleasant when they talk to a woman at the gym (e.g. touching without asking, getting way too close etc)...
And one last piece of advice: (Preferably) do not ask her for her number but rather give her your number. This lets her decide whether she wants to contact you or not.