A tourist visa means you're a tourist, which means you're legally allowed to be in the country, but you're not legally allowed to work. There are many visitors that work anyway when they just have a tourist visa, and generally immigration doesn't crack down, but if you're planning to pick up work bartending or waitering, give it serious consideration. Sure, you'd like to stretch out your funds and be able to support yourself, but Honduras has a high unemployment rate, and you'd be doing a job that a local could do. There are many travelers that work as dive instructors, which there are very few local instructors, and others that teach in a few of the more expensive bilingual schools, as there aren't many well trained local English teachers. There are also lots of possibilities for volunteering- you won't be making any money, but you'll be giving back to the community, getting a completely different experience than just vacationing, and having lots of fun.
If you want to get proper legal status to be able to stay longer term (and to work), then you'll need to check with a lawyer, as both work visas and residency need to be done through a lawyer. Do your homework on which lawyer to use, because having a bad lawyer means lots of headache and wasted money (my first one took half my payment, and then never completed my paperwork, so I eventually started from scratch with another lawyer). Work visas are rare- they're about as costly as residency (around $2000 or more), take about 6 months to attain, and tied to the company that you're working for, so if it doesn't work out with that job, you're back to square one. There are several types of residency, so this is the route that most people opt for. The lawyer will be able to tell you the different options and requirements. It's not cheap, and it takes time- several documents like police clearance you'll need to get from home, and might need to have authenticated at the Honduran consulate in your home country (your lawyer will know all the current requirements). Residencies need to be renewed, most of them on a yearly basis, though there is a class or residency that just has a 5 year renewal. The renewals used to be done in La Ceiba, but just recently, there's now a place to renew on the island. It's not expensive to renew, but you'll want to make sure you're bringing in the correct paperwork
Once you're all set up here and get a job, there are government deductions. Taxes, healthcare and something like a pension plan that gets deducted if you're working for a larger company (I think a company of 30+ employees). If you're setting up a business, you'll want your lawyer's help with that as well, and then get an accountant to handle your monthly tax payments for the revenue, as your yearly income tax.