A great difficulty here is that there's not really much in the way of "professional beta readers." Someone who's really known for giving excellent feedback, and offers that as a service, is pretty much an editor of some stripe.
So aiming to become "well-known", "popular", or "respected" as a beta reader might not be in the cards (although it's not impossible!). And turning into something paid is... well, it's really hard, because it's asking people to trust and pay you, in an area where it's really hard to Show Your Work, and where you've got a lot of competition that's a lot safer.
But you can certainly become a good and busy beta reader. And that's pretty darn doable.
Beta-Read on Online Workshops
This is something anybody can do. Sign up to Critters, dive into Absolute Write, check out Scribophile -- all of these give an endless supply of material to beta-read. Some of them have even more: community, social connections, and/or guidance on becoming a better beta.
There is a catch: this is mostly going to be amateur work; often painfully so. For two reasons:
- Most writing is amateur work. There are a lot more people who want to be published authors than people who are published, so you're going to have a lot of very unpolished material.
- Pro authors level themselves out of the big general slush pool pretty quickly. Basically, you find five people who (a) you get along with, (b) are happy to beta-read on occasion, and (c) you find helpful -- and you never have to enter the crapshoot of an online public workshop again.
BUT. If you're just getting started, then working with amateurs is great. It will let you learn. You'll be finding your feet, learning your own taste, and figuring out how to give feedback that's helpful, constructive, and clear.
And, the fact that most of the work will be amateurish, doesn't mean you won't find absolute gems. I certainly have.
Establish a Niche Where You Can Form Connections
If you are active in any community that's even partially related to writing, you can often do really well by making connections within a small, focused group, that would be much harder if you were just hanging out your shingle for anybody in the world.
If you have any particular hobbies or fandoms, some of those people probably like writing. If you are, as so many of us are, living in a particular geographical location, there are probably a whole bunch of writers nearby. Maybe they go to the library; maybe they already have critique circles you can join.
What's nice about these is that they're personal connections that last much longer than the critique of any one manuscript or story. Make a good connection with one writer, and you'll probably get to beta-read a whole bunch of their work. You'll be friends on social media, and see when they're looking for readers. When other people are looking for readers, your friend can point them to you. Actual connections get you far.
Hang Out On Bookish/Writerly Social Media
There is so much of this, and being involved will drop opportunities in your lap. People who need beta readers will ask for them -- and you can volunteer.
Follow authors you love. Follow authors who say interesting things. Follow newbie authors writing about being a newbie author. Join social media groups for writers. I've gotten a bunch of really interesting reads, just by following some awesome people, who pointed me at something interesting that one particular time.
Consider Slush-Reading or Reviewing
Neither of these are the same things as beta-reading. But they will work on the same muscles, and they'll also put you in the right arena -- meeting writers, establishing a reputation.
Slush-reading means reading unsolicited short story manuscripts for a magazine, and writing up comments to the editor. It's much briefer and coarser-grained than beta-reading -- but it is evaluating manuscripts, and even working with an editor (to some degree). Check out magazines (especially online magazines) in fields that you like. See if they're open for applications.
And reviewing -- anybody can open a blog and start reviewing. Gaining an audience is much harder. But you can start out for practice, and to build yourself a little online home-base. And, you might consider looking for existing, established sites which publish reviews. Again, a review is very very different from a beta-read -- it's aimed at the readers, or at prospective readers, not at the author -- but it's still a very helpful skill to develop.
Talk About Beta Reading
Let people know! Tell friends and followers that you enjoy beta-reading, and that you'd love them to send material your way.
Especially tell this to writers you beta read, and especially the ones you enjoyed working with -- they're likely to write something else next, and you'd love it if they went right to you and wanted your feedback.
I hope this helps make sense of things, gives you a sense of options, and offers some concrete things you can do next. All the best!