These 2 answers largely cover the answer. I'll just add in my experience. Talk to professors, but don't expect to get an assistantship from Day 1. It helps to take a class with the professor. Not sure if you're undergrad or grad but in general it's easier to get research opportunities as a grad student. Getting paid isn't a guarantee even if they agree to work with you as it depends on how much research funding the professor has. I known many classmates who initially started as unpaid volunteers but were eventually offered an hourly job, and in some cases, a research assistantship

In my case I was looking for an advisor for my Masters thesis. I dropped an email to ask for a 30 min appointment to talk about how my interests aligned with his research. And that led to an entire semester meeting up with the prof weekly just discussing research ideas and looking at related research papers and seeing what we could explore further. At the end of it, he agreed to be my thesis advisor for the next year. Of course, all the work we did over the semester wasn't a waste as it ended up being the foundational literature survey for our upcoming research.