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.
I was literally just talked to a mentor of mine the other day about this and he gave me a great little idea.
A quick test: Put up an ad on Craiglist about your service/product whatever. For example, if you want to know if people would pay to use your backyard for children's parties you could say "Great backyard available for kid's parties. $50/hour + free access to kitchen and bathroom. Contact me for details." See how many folks email you with willingness to pay. If they do, cool, you have a profitable business idea. If not, maybe re-look at your model. (This could also work with Google ads, Facebook ads etc. Just let anyone interested know that the idea has fallen through and you'll keep them posted.
I believe this idea was taken from App Sumo: http://www.appsumo.com/sumo-business-blueprint-live/
I've also heard good things about utilizing Google surveys.