PROOFREADING COMES at the end of the editorial process. It's the very last check through, designed to find any typos, punctuation & spelling mistakes, grammatical errors and inconsistencies in text. There's no content or structural edit involved in proofreading because it's a proofread, not an edit. Different process; different part of the brain.
While editing and beta reading will generally pick up on errors, a final and dedicated proofread is recommended for any type of submission or publication. If you're lucky enough to have a grammar fiend for a friend, they're worth their weight in gold.
It doesn't matter how perfect your script is, it's essential to get an outside perspective on it. A good beta reader will pick up an error that you could have sworn wasn't there. Joining a writing group can be invaluable, especially if it means reading your work aloud. There's nothing quite like an audience to highlight those punctuation mistakes. As writers we're too close; we can't see the trees for the woods.
WHEN DO YOU NEED A PROFESSIONAL PROOFREADER?
I like to say that every script could benefit from professional proofreading, but the truth is that a dodgy semicolon isn't going to put a potential agent off. Publishing houses have their own dedicated team. This doesn't mean you shouldn't get an outside eye on your work. A grammar fixated work colleague might not know a character event horizon from a fractured story arc, but when it comes to proofreading they're your new best friend.
However, if you're self-publishing, there's a VERY small gap between your finished book and your potential readers. I've seen too many substandard self-published books. Having a professional attitude towards editing and proofreading lifts you above the crowd. This is your brand, make your choices count.
Proofreading is usually charged by the word. Although I tend to pick up errors as I edit, I wouldn't claim to be anywhere near good enough to proofread a novel. Recommendations from other writers are best. The society for editors and proofreaders has a directory. If you're stuck, contact me.