You hear these terms: "CP" and "Beta" tossed around a lot, and if you're new to the writing world, they can be confusing. Let's define them first, then talk about how to find good ones.
CP = Critique Partner
This person is sometimes referred to as an "alpha reader." They read your work in the early drafts, they advise you on making big, sweeping changes. They are your support system when you need to cry, when you need to celebrate, and when you need to brainstorm.
My CPs get regular emails, asking questions about "Wait. What if I changed this, is that crazy?" By the time the book is ready to query, they've read it probably three or four times and they deserve all the love in the world. They need to think like a writer.
(Full disclosure: One of my CPs is not a writer - she's just the most perceptive and honest reader who has more patience than Mother Teresa)
This is also a two-way street. I read their stuff with the same amount of honesty, and I want to see them succeed as much as I want to succeed . These are the people who will read all my books, and I will read all of theirs.
This person will read a near-ready version of your book. They're usually part of your target demographic (i.e. - if you write middle grade, at least some of your beta readers need to be twelve years old, if you write young adult, you'll need to find actual, living teenagers to read your book). If they aren't your target demographic, then they read extensively in your genre and category.
Beta readers will make inline notes, checking for typos and such, but that's not really their job. From your betas, you'll basically get a thumbs-up or a thumbs-down on the big stuff. Is the book any good? Do they like the characters? Why or why not? Does the world make sense? Things like that.
You'll still make at least one round of edits after your betas finish reading, and I know more than one author who has gone back and done full rewrites after the beta round.
Where do you find them?
They are all writers or readers, so you need to be places where writers and readers congregate. On the internet, that means twitter. In real life, it's writing groups and book clubs.
Try people you talk to often, or just tweet "I need a CP/Beta for a <category> <genre> that's about <# of words>. Any takers?" People will answer. If they don't, go follow more people, get to know more people, and try again.
CP Seek is a website where you can find people who want need critique partners and are willing to trade manuscripts. I found two of my very favorite readers, who write some of my most very favorite kinds of books, on CP Seek. I also found three who didn't work out so great - not anybody's fault, we just weren't a good fit for each other.
How do you know if you're a good fit?
Ideally, you'll have similar reading tastes. If I met somebody who hated Harry Potter, loves to read Tolstoy, and just doesn't understand Star Wars... we are not going to be a good fit. And that's okay. There's a CP out there for everyone, and you don't need someone who is going to accidentally insult your work simply because it's not their style.
You should also read pretty heavily in each other's genres and categories. I write adult fantasy, but I also read a lot of YA science fiction and fantasy, so I understand the differences and why something works or doesn't in YA. I don't read MG well, and I don't do literary fiction. At all.
One reader got a hole of my manuscript and wanted me to slash 25-30K, basically cutting everything that wasn't main plot or dialog, and even that needed to be shortened in her opinion. She didn't read adult fantasy (the MS in question was under 100K, and well within industry standards for the genre and category), she read YA contemporary, which is very dialog heavy, and short on word count by comparison.
She's a very good writer. She's a good reader. For someone else. Don't put yourself in that position.