Write Away

If you're talking about a beta for a whole novel, send them 2-3000 words first and see if your styles match up.

A whole novel is a lot for just one beta to edit - they're not getting paid, after all, and you haven't done beta yet for them in return. Be prepared to work with a succession of betas rather than just the one. That might turn out better, anyway, as each beta will notice different things. They can skim read the parts that come before. A good beta takes time. Make sure you leave enough for them to work. I estimate an allowance of one day per thousand words, once they've already agreed to do it.

Always feel 100% free to disagree with everything your beta says. A good one won't mind, and that disagreement can be really useful as it sharpens your focus about what you want to achieve (and probably aren't hitting quite yet). Although complete disagreement is probably a long term sign you aren't suited to each other.

Be prepared to find that wait between sending your story to your beta and opening the result back from them horribly, stomach turningly nerve wracking. It always is for me, but invariably worth it.

In my experience, the best way of finding betas is to
a) ask for them on beta search comms
b) first do beta for other people and then ask if they're free to do one in turn
c) join some kind of writing challenge or community which matches writers and betas as part of the process.

Other than that, what everybody else said. Have a clear, detailed exchange about what you both want from the process before you start.

Ideally both of you should read some of the other's work first, even if it's just a couple of blog posts. Then at least you have similar ideas about basic spelling and punctuation - not always a given.

One last note - don't forget to tell them what kind of English you write in, eg American, Australian, Hong Kong, UK. Don't just assume they use the same as you do.