Every business is different, and there are probably different requirements depending if you're a bar, restaurant, dive shop, or hotel, but usually the start of any business begins with a trip to the lawyer. Find a good one, because having a reliable lawyer and accountant make a big difference. Generally you'd want to create a corporation, though it's apparently also possible to start a business as a comerciante individuale, though I think there's less flexibility with the second option (I was recommended to start a corporation). Once you've formed a corporation (this is pretty much all work for the lawyer- at the end, you'll get the legal document of your corporation), then you'll need to get an RTN number for your business (you also need an individual one). You used to be able to get this at the Zolitur office in Roatan, but apparently now you need to do it in La Ceiba. It's been awhile since I went through that process, I think you'll need to take along your corporation document as well as your ID.
To get your operating permit for your business, the municipality will give you the list of requirements (inspection from the fire department, inspection from the municipality, copy of land documents and a rental agreement if not on your own property, corporation document, RTN number- not sure what else is on the list of current requirements. There have been recent changes, now requiring that all businesses are members of the chamber of commerce, and any tourism based business is member of the tourism association, both which have yearly fees in addition to the fee for the operating permit.
The operating permits are based on a calendar year, so no point starting up a business at the very tail end of the year, might as well get yourself all organized to start at the beginning of the year. Once you have your permit, you'll need to get specialized receipt books: the requirements of these also frequently change, and they have expiry dates on them. For example, the government just changed their requirements, giving businesses 2 weeks to have new receipt books printed in accordance with the new requirements, with all old-style receipts no longer being valid after that date. Even if you had just gotten some printed, they'll all need to be turned in to be destroyed.
Your accountant may help you to get your receipt books (mine does for me). At the close of every month, the receipts need to be turned in and monthly taxes that have been collected must be paid, within about the first few days of the next month. My accountant does this as part of his monthly charge: I pass him the receipts from all of my expenses, the government copy of all receipts issued for customers that month, and the taxes due, and he takes care of filing the taxes. Every year, he also does the annual personal income tax from the business, which I think gets done in March or April. Occasionally the accountant will contact me with a new hurdle to jump, whenever there's some change or the other with a government agency and more paperwork of some type is required. Generally everything can be taken care of right on Roatan, though last year I remember there was some new hoop to jump through, with the government representatives on the island just a couple days for appointments, and the line up going out the door, down the stairs and along the road, so for that one, I took a trip to their La Ceiba office to handle things instead.
For me, having a business in Roatan has been a great choice. Though the sometimes convoluted processes and changes from the government sometimes don't make much sense, and being a small business owner sometimes means extremely long days, I love what I do, and have gotten such enjoyment out of growing my business and meeting people from all over the world. If you're thinking of taking the plunge and opening a business in Roatan, I wish you the best of luck! Feel free to contact me with questions about my experiences, I'm happy to help out if I can.