Have them sign a contract, there are lots of samples online.
Try to do the work hourly or set a fixed fee for a well defined scope of work (break this down in to milestones). With Rails you could probably package up one or two milestones of the auth, models, etc that you can complete quickly to show good progress, and good profit to get things started.
If they change anything from the initial scope send them an authorization to add a milestone and cost for that addition, before starting on it.
Set everything up with incremental development/review/ok/payment (even if it's hourly).
You should also require a retainer/initial payment to make sure they are serious. 50% of milestone 1 or what your first invoice would be.
Break the project up in to parts you can complete in a week or two. Then invoice incrementally, get his ok on that portion of the work and the payment then move on to the next portion of work.
DO NOT work too far ahead without sending an invoice, invoice often especially early on (for hourly I would invoice at least once per week till you're more comfortable with how easy the client pays you).
Getting their ok/payment is important, occasionally you'll get near the end of a project and maybe it's not turning out like they expected or they didn't include everything they needed in their scope and they will start trying to say it's unacceptable and start talking about a refund. That said, be prepared that they might decide not to continue the project after a few portions/milestones, which is ok, as long as they pay for the work you've completed.
Also if they are difficult to work with you might want to pull the plug on things after a couple milestones.
Also set it up so the source code resides on your hosting for his review until the project is completed. Release it on final 100% payment. (You can email send them a zip of your repo after each invoice is paid before starting the next milestone).
You can note these things in your contract.
Get an EIN number (Free from IRS), you can use your name as your business starting out. You use your EIN in place of your SSN. For your W-9 that they should request you fill out if you make over $600, regardless report all consulting income on your taxes next year whether they send a 1099 or not.
http://www.irs.gov/Businesses/Small-Businesses-&-Self-Employ...
For payments you can use paypal. They could always try to do a charge back so keep that in mind.
Checks are typically ok, just keep in mind they might take a week or two to clear their bank, if they bounce those funds will be pulled back out of your account.
Typically you won't have an issue with people, most clients pay on time, occasionally you'll run in to a bad apple. Usually you'll get a bad feeling about a client, or see a red flag, it's best to pass on those projects/clients.
Good luck with your first freelance gig.