Market Research is near and dear to my heart, although I won't claim to be the world's foremost expert on the topic. What I can tell you is that there are many different approaches, and that the details vary depending on whether you're doing B2B / enterprise, or consumer facing web apps, or mobile apps, or retail goods, etc.
But the basic point is to identify some "segment" ("redheaded boys between 9-13" or "mining companies with > 5000 employees" or "whatever") that you think might have the problem that you think you are solving. Then talk to a subset, but a large enough subset to get some validation, and find out if they actually want / need the thing you're proposing to build.
Then, if you find that some percentage do want it, you can try to extrapolate and do some rough "back of the envelope" math to see if it's worth moving forward.
Example: You find that about 33% of the redheaded boys between 9-13 that you talk to, do want your thing. Be conservative and round down to 25%. Then find demographic data on how many boys between 9-13 there are, and then find out what percentage of the population are redheads, etc. Run through all of that until you have a (very rough!) number of potential customers. Say it's:
14,237,984 redheaded boys between 9-13, and take 25% of that, and you have a market size of:
3,559,496
Hopefully your validation process gave you an idea of what price you can charge, so let's say you found out you can charge $20 for this thing. So you're looking at potential revenue of $71,189,920. Of course, you probably can't sell all of them in one year, and once you exhaust that pool, you're down to factoring in population growth and birth rates, etc., so see if the influx of new boys in your age range is going to keep your market alive after the first push.
Also, assume it costs $8.00 to build, and there's overhead for distribution, etc., so let's project a per-unit profit of $10.00
So you're looking at a potential profit of $35,594,960.
Now figure out how much capital you have to invest, figure out the opportunity cost of your time, and decide if it's worth chasing that $35,594,960 in profit.
Note that all of these numbers are totally made up, and the only point I'm trying to get at here is how you develop a very early, preliminary "go / no go" decision. If that initial number came out to $5.00, or negative, then it's an obvious "no go". It it comes out to a trillion dollars, it's probably a "go".
I would like to be able to interview more consumers/businesses, but that has been difficult to orchestrate.
Some of the numbers I mentioned above, for consumer apps, are available from the govt. or other public sources. Population data, demographics, birth rates, etc., are usually available. What you'll have to put some work into is finding that population sample to validate your hypotheses against. That takes elbow grease and feet on the street. I don't know any easy way to short-cut it. You can get some mileage out of surveys, focus groups, etc., but nothing beats actually talking to people.
You may be able to cheat a little bit by using Google Hangouts, Skype, and other tools to avoid having to physically meet people, but you still want to talk to them if you can.
One last caveat about the above scenario.. it's intentionally over-simplified to make a point. I left out a lot of other issues you'd need to factor into evaluating your market, like income levels, education, cultural issues, etc. That's why I say the first number you will come up with is very preliminary. Basically you want an answer to the question "is this even viable in the very best possible case"? If the answer to that is "no" then there's obviously no reason to bother. But you'll rarely experience the very best case, so you'll have to continually be learning and re-evaluating things as you go.
Finally, if you haven't done it yet, I cannot recommend reading @sgblank's book The Four Steps To The Epiphany highly enough. He touches on a lot of points related to figuring out of a business is going to be viable or not.