When: I'm still experimenting with this. In the past, I have waited to
Where: Okay, I just put that in because it's part of the litany. But I could make it an answer about where to find a beta-reader. I find them at work. Try the PTA meeting. Your book group (I at one point managed to get my book group to read my MS and offer critiques. They were very kind, somewhat helpful--and out of that experience I connected with two other writers to form a writing group that is still the basis of my editing exchange).
What: The "what" changes as you work through the project. As noted above, you might want someone to kind of do a reality check early on, and let you know if you should continue or rethink. Later, you need the various forms of editing on the finished draft.
Why: If you have to ask this, you probably should keep your day job. Seriously.
How: This one's the killer for us Indie folks. We don't expect to make a lot of money from our books, so shelling out the big bucks for a pro editor doesn't seem very feasible. So here's my take on it: while a pro is probably best, any reasonably competent editor is better than none. So you find a grad student in the creative writing program or a wanna-be English teacher, and work out a deal. Maybe they aren't perfect. But they will, if at all competent, be able to tell you where your story stops making sense, and when you've changed point of view three times in a single paragraph. Join a writer's group and let them critique the work. And finally, your proofreader could be anyone who is really good at spelling and details. Actually, it's not so much about spelling (your spell check will tell you it's "weird" not "wierd") but about knowing the homophones, having a good vocabulary they can gently point out that you meant "ablution" not "ambulation" or that most likely in 1873 they didn't use the expression "put the pedal to the metal." Ask your Mom or that cousin who always sends back your email with corrections.
Oops, I think my "how" drifted back to "what." Where's an editor when I need one?