How to Get Paid
I want to break down the basics on this. I was shy about asking for this info when I started, but now I ask everybody, "So...is it okay for me to know your rate?"

How much to charge
When I started in advertising I was billing at $350 per day. Within a year I think I was billing at $500, and gradually I climbed up to $850 for illustration and $175 (per hour) for consultation–where I am today. There are some storyboard and sketch artists making up to $1000 per day. I'll probably raise my illustration rates in the fall to $900. I could push it a bit further but I'm most comfortable working in about the 80% percentile. It helps me mitigate stress and gives me confidence that my clients know they are getting great value for money
Per day actually means eight hours in my case, so the actual amount is prorated to be higher or lower depending on the real hours spent. Weekend rates are $1275, which is time and a half. It can become more complicated with book illustration or anything with profit sharing. There should also be a whole other post on what a "hold" means and communicating about booking.
Here's what that rate covers
I charge for all the time I spend directly relating to the project. That includes emails, phone calls, and reviewing materials. There are a few exceptions. If a project seems outside my normal purview, I will sometimes offer to do a sample or a bit more research for free before agreeing to take it on. I don't charge for the time it takes to negotiate terms or booking, or for providing a quote after a quick discussion about the clients' needs and expectations.
But once the clock is ticking, so to speak, I'm charging for the meeting time, emails, and of course, drawing.
There have been a few cases with individuals and small companies where I've spent so much time working out a plan with them over email that I eventually turned down these jobs. In these situations, the available budget was already too small for what they wanted drawn, and the time it took for me to uncover that fact turned into a few hours of unpaid work.
Sometimes you'll get the intuition with a client that they either can't actually afford you or are penny pinching. If you've heard of the saying, "Don't throw good money after bad" you can just apply that to your time. Repeatedly explaining to clients why their budget isn't enough for the laundry list of drawings they want may take three hours. After negotiating the work load down, it would be a shame to then book that eight hour day of hectic crazy work just to make the previous three hours worth it. Not only will you still technically never get paid back for your initial time investment, those are probably also the clients who will underestimate the added time needed for their inevitable revisions. Then you'll have to have the budget discussion all over again.
The truth is I wouldn't mind getting a lower rate from smaller companies. I want to promote that type of business. The biggest issue for me is that low budget projects clients have historically stressed me out and undervalued my time the most. And by that I will not abide!
When do you get paid
If you're booked by an agent, you'll receive your money minus the agent's commission, one to three months after completing the project. For projects lasting two or more weeks, it will be billed in segments. If you're working directly with a creative agency, you get to negotiate the terms. Thirty or sixty day invoicing is pretty common. I often receive a check within two weeks regardless of the invoicing schedule I send.
Dine and dash clients
In my experience this happens very, very rarely. More often smaller firms just forget to send the check and you have to remind them. I send an invoice when I've finished the job. On that invoice it says they have thirty days to pay me. If I don't receive my money in thirty days I send them a friendly reminder, they say, "so sorry!" and I usually get the check a week later. I have one client I really like who always forgets to pay me. When I remind them, they'll say something like "Oh really? The check is in the mail so you should get it soon!" When I receive the check I can see the post mark is actually for a couple days after I sent the reminder email. This has happened repeatedly and it always cracks me up.
On only one occasion was a client vocally unhappy with my work. That client then asked for a partial refund. I was pretty taken aback, but I gave them something like 10 or 15% off and never worked with that person again.
Another time, I did a guy a favor and drew something on the cheap for him. He only paid for half. I reminded him that he owed me $50 and he stopped responding to emails.
The fact that I can name the two times this sort of things has happened, sure assure you that it doesn't happen often.
How to find your own rate
There are some online resources out there, but another thing you could try is finding people who do what you want to do, and then just asking them. Some people won't respond, others might feel uncomfortable, but you may be surprised how many people are actually really happy to help. I'd try something like:
Hi, my name is Kiva. I want to be a storyboard artist. I found your website online and I see that you're in the industry I'm hoping to crack into. I've worked hard on my portfolio but a few things are still pretty mysterious to me. I was wondering if you'd mind sharing advice on how much I should charge. Thank you, sincerely, blahblahblah.