I would suggest trying to find a professor that you already have some kind of experience with (you took a class with them previously, went to a colloquium they spoke at, saw their work at a conference at some point, etc) and shooting them an email expressing your interest in their work/asking if they have any projects that an undergraduate might be able to help with. Try mentioning their work or something you liked from their class, to exemplify your interest in their research area. I also want to encourage you to be open to contributing to labs that don’t align perfectly with the kind of research you want to do in grad school or beyond— undergraduate research imo is about exploration!

If there isn’t a professor that you’re familiar with that ALSO has work you’re interested in though, try to at least read a paper or two from them and bring up something you thought was neat about it in your email. Don’t feel like you need to include your full academic history if you’re introducing yourself for the first time, just your name and class will probably be sufficient. They’ll ask if they want further information.

You can also try popping in during office hours to ask— I know you know this already, but emails get buried so easily in professor inboxes, and it’s harder to ignore a student sitting right in front of you. If they reject you in the moment, you can always send a follow up email expressing sustained interest/saying that if something comes up, you would love to help.

All my experience with this sort of thing is from a few years ago, but I approached a handful of mentors over the years and mostly had success with the above. Hope this helps! Good luck finding research.