This question is very broad so it's tough to answer, but I'll give it a shot.

Is there anyone else making money in that market? If so, how? What business models are working well?

Take the automobile industry. There are hundreds of business and revenue models in the auto industry (wholesale, retail, repair, parts, leasing, specialization, etc.)

There is potential profit in every market, it's the intersection of the market and your particular business model or product / service that determines the profit.

If you can be more specific, I can give you a better answer.

Simple answers depending on what your product is:

1. Post the product to eBay and test pricing
2. Post it to Craigslist
3. Ask all your friends and family to buy it
4. Take 20 people out to lunch that are in the target market, tell them that in three weeks you are planning to launch a business that sells x. Ask them a lot of questions about their needs as a target customer - but do not sell them at all. At the end, ask if they know anyone who might be a good fit for your product.
5. Create landing pages and test them with Google Adwords, Bing Ads, or Facebook ads. Get the sale but do not charge the credit card. This is relatively low cost, gets fast results, and is my specialty - I'd be happy to help.

Cheers -
Nick

Entering the market in proven categories that show success is a great place to start. There are tons of problems that currently need to be solved and services that customers are looking for. By finding the answer to a problem that already exists, you automatically have interested customers, and you do not have to search for them yourself. With the number of choices that are in the market, you are more likely to get your current customers to purchase a new product then try and attract new ones.
You can read more here: https://blog.marketresearch.com/how-to-determine-if-there-is-a-market-for-your-business
Besides if you do have any questions give me a call: https://clarity.fm/joy-brotonath