I'm a cis-gendered female, but people used to mis-pronoun me a lot as a teenager. I usually just ignored it, unless I knew it was someone I was going to have to deal with long-term.

I'd like to correct them, but I feel impolite even though it's they who are being impolite. So I usually don't do anything and will at times will take them aside if we're in private.

Usually I ignore it mostly because i'm not assertive
and because a lot fo my family doesn't know- I'd hate to out myself to them

Usually it's a mix of waiting for someone to correct them or I ignore it. But ignoring it doesn't help because it still makes me feel like shit when someone mis-pronouns me.

I've I've caught others using the wrong pronouns for someone, I wait a few seconds to see if that person will correct them, but if they look awkward or don't say anything, I'll correct the person. Sometimes people are embarrassed to correct people on that sort of thing, and I don't mind stepping in for others if they don't speak up for themselves. If I catch myself using the wrong pronouns or the person corrects me, I apologize profusely and try harder to remember in the future.

Usually I'll ignore it if it's an innocent error, but otherwise I'll say something.

If it's a stranger I usually pretend it didn't happen, or put on a deeper voice. One of my coworkers corrects people for me, so when I'm working with him, I wait for him to correct them for me.
However, when it's friends and family I correct them

I don't really mind what pronoun is used for me so I usually don't say anything but my partner has the singular they pronoun and I politely correct them afterwards.

It depends on the situation. If I'm not going to see this person again, I don't usually bother correcting them. If it was a friend, most of them are really good about pronouns and if they slip up I can usually just give them a weird look and they'll correct themselves.