Alright, so..... sounds like the plan is to teach a few classes a week at the grange hall. So you have your location worked out, which is one hurdle you've handled.
I think first off, even as a part-time venture, if you want it to succeed and make money, you need to learn some general things about how to start and run a business. Where I live, the county SBA (Small Business Administration) branch offers free classes a few times a month about different aspects of starting or running a business. Everything from "should you be a sole proprietorship vs LLC vs corporation" to "how to use Facebook to advertise your business". You may want to see if there's something like that where you live. You can probably get some of the same information from books, but it's nice to actually talk to people.
The first class topic I mentioned there, about what kind of business structure you should form your school as, is one that you need to look into before you start. I'm honestly not sure what the best choice would be for someone doing this part time. I'm guessing that it would be more hassle than it's worth for you to incorporate at this point, but you should look into the pros and cons of different business structures and decide for yourself.
Like others have said, you'll want to get liability insurance for you/your business, in case someone gets hurt and wants to go after you personally rather than grange hall. There are lots of companies that offer martial arts insurance. It will run you at least a couple hundred bucks per year, but they may allow you to pay in installments.
You'll also want to make sure you have a website and do some advertising. Maybe a logo, too.
Beyond that, you have to think about your actual martial arts program. You'll need to consider things like:
1) Who are you teaching? Adults, kids, both? You may want to set up different classes for different age groups, if you're planning on teaching both kids and adults.
2) What is your curriculum? You need to set up a curriculum that says what needs to be covered at each belt/sash/level.
3) How will you teach those different topics and techniques that you have in your curriculum? (a.k.a., lesson plans)
4) What kind of equipment will I need for these classes? Since you're using a community space, you'll also want to consider where you'll store the equipment and how you'll transport it to and from the hall.
You'll also want to consider:
1) What fees to charge your students
2) How to collect those fees
3) How to keep track of your students and their memberships (and whether they've paid you)
For #3, I'd recommend getting a student database program/service. Some of these (MindBody, Zenplanner, etc) cost a good bit of money, because they also handle billing, online registration, allow your students to check in with a bar code scanner, etc, which I think is a lot more than what you'll need at this point. I've heard that OpenBlackBelt, I think it's called, has a free version with more limited features. As for payment, for now you can probably just ask your students to give you a check every month or quarter, and use your database system to keep track of when they pay.
Okay, I'm running out of steam here. But I hope this helps.