Beta Reader
Being a Beta Reader
Constructive Criticism

I think the first one answers your question, but just to be sure: usually, someone who needs a beta will post a request on the Board providing basic information about the story. If you're interested in beta-reading, you post a reply saying so and provide your email address. The author will then contact you with further details about what they're looking for from the beta process and, in most cases, an invitation to comment on the Google Doc where the story is located. (I don't think there's anyone here who doesn't work in Gdocs at this point.) You make all specific suggestions for improvement of SPaG and such in the doc, and possibly sum up with general impressions by email.

DON'T post beta feedback about unfinished stories to the Board. Reviewing finished stories on the Board is great and highly encouraged, though, and utilizes much the same skills!

Actually, if you're interested, I have an interlude cooling its heels in the beta pool at the moment (my other beta is a busy person). If you want to jump right in, I wouldn't mind you having a look, and I can help with any other questions you have about the process and the PPC. {= ) The story is about one of my most established characters, Supernumerary, but it happens to be based on one of the Permission prompts, "The agent(s) have to recover a lost [child, in this case] in their care." I don't think you'd need much, if any, prior knowledge of my spin-offs to follow it.

Either way, welcome!

~Neshomeh