A beta reader is usually a test reader of an unreleased work of literature or other writing, who gives feedback from the point of view of an average reader to the author. The beta reader’s job consists of commenting on the flow, plot consistency and characterization of the story. This feedback is used by the writer to fix the remaining issues within the story.
When a badfic is being reviewed by a member of the Canon Protection Initiative, the reviewer will often suggest getting a beta. When writers claim to have one when their fics are riddled with errors, it is insulting to their readers, themselves, and their betas—if they do actually have them, which we have to doubt.
A good beta reader should be treasured. That means taking their advice, or at least giving it some very careful thought before deciding not to take it. Showering them with gratitude and praise, possibly in the form of chocolate, doesn't hurt, either.
The PPC grants free beta services to most people who ask for it. We used to have a beta chain, but it is now largely inactive, except for the occasional proponent of Viagra or some obscure dating service.
How to Find Beta Readers
Just post a beta request on the Board, but beware: Although a Board post is only visible for a limited time and you will not get many readers through a link on the Board, posting a link to a story on the Board is considered to be publishing nonetheless. You probably don't want to be humiliated by having all your failures discussed in public, and for some beta readers it may be difficult to be honest when they know that everybody can see what they only want to say to you.
So, do not link to your story when you ask for beta readers, but give the Boarders enough information so that they can decide whether they are able and interested to beta-read this story. Potential beta readers will respond to this request, telling you their e-mail address or other ways of private communication.
You then contact the selected beta reader(s), providing them with an address to send their feedback to. If you have a share-able document (e.g. Google Doc), you can just send them the link. Remember that not everybody may have an account and be able to log in. It's best to share the document with everybody who has the link, which should only be your beta readers anyway. You may also want to enable commenting for everybody who can see the document. Thus, rather than sending you long e-mails quoting the document to point you to where their comments apply, your beta readers can attach comments to selected parts of your document, and you can answer to the comments if further discussion is necessary. When the last cycle of beta-reading, commenting and editing is finished, you can hide/remove all comments, disable commenting and then proceed to posting your mission report.
In case you cannot share your document, or your beta readers cannot or do not want to work with a shared document, you can send the document as an attached file with your e-mail. If they didn't already tell you, ask your beta readers which file type they can or prefer to work with. Common file types are .docx (Microsoft Word), .doc (old versions of Microsoft Word), .pdf (Acrobat Portable Document Format), .odt (Open Document Format)...
There is also a way to get the attention of potential beta readers who do not check the Board every other day: Look their e-mail address up on the PPC Wiki's list of beta readers or in the beta readers category. (These are also the places to go if somebody responds to your beta request on the Board, but assumes that you already know their e-mail address or can easily find it on the Wiki.)
You may not be comfortable with e-mailing a stranger out of the blue, but since they put their address on the list or on their user page just for this purpose, we may assume that they are not uncomfortable with this. However, be prepared to be rejected or never get a response at all; there is a lot of outdated information nobody dares to remove because there is still a chance that an inactive Boarder may return. Try to contact persons who fit your requirements (e. g. know the continuum) and who you have seen at least occasionally on the Board or in the IRC not too long ago.
We had a workshop on beta reading. Check it out to see what you can expect from your beta readers and what they expect from you.
How to Be a Beta Reader
We have a workshop on this.