How do academics make money from applying their research?
I mean if I was a very smart researcher, and discovered something that no-one has known before, then first thing for me would be to create a company and sell it.
Come on, do you even think it is so easy for someone to start a company and start making money? The skills needed to make a product (corporate world) are different from those necessary to create an idea (academia). A simple well-thought out, well-exposited algorithm may bring plaudits in academia, but in the industry you need to implement the algorithm as a small part of a large system, subject it to rigorous testing, find people to market the product and suitable customers to buy, etc. And then there is the whole HR team which has to do its thing...
Patents are the way to go if you have to make money from a smart idea in the academia. (EDIT: Generally, both the University and the inventor share equitably the royalties and other income arising out of inventions developed under University auspices.)
Professors do engage themselves in collaborative work with the industry; at times, they are funded by the university for setting up small companies (see this question.). The lifestyles of people in the academia and the industry are vastly different; for one, professors have much more freedom with respect to timings than in the industry and afford greater time for their family - not a bad thing in exchange for money, after all.
Successful researchers in academia are unlikely to quibble about low income compared to people in the industry. Happiness versus money is a concave function - beyond a point, more money is unlikely to make one happier.
From my experience, most researchers who choose to make money do so in one of two ways:
Entrepreneurship. Take whatever you've found with your research and start a business somehow marketing it. This is a common path, as you are the expert in your field, and you can bring it to market in ways that no one else can.
Many researchers do not follow this path, though, because the skills and interests required to run a successful business are oftentimes very different from the skills required to become a successful researcher. Anecdotally, the majority of researchers I've met were not interested in bringing their findings to market in any way; they just wanted to perform research and not have the headaches of running a business. Note also that you will have to inform the university about your business, and you will have to deal with the conflict of interest problems that arise because your research affects your business.
Consulting. This is a much easier path, and is performed by many researchers in a variety of fields. It is unlikely you will strike it rich doing consulting, but it can bring in a significant amount of extra cash.
A subcategory of this is legal consulting. I put this separately simply because it's consulting of a completely different nature that most business consulting. Depending on your field, you may be able to be called in as an expert witness in a legal case, which can also bring in extra cash. This is less common, simply because of fewer opportunities.
There is a lot of reasons leading to the fact that academics don't necessarily start a business each time they have an idea that seems to work:
- There is a very long and difficult (technical) path from an idea that works to a product. Finding the good persons for following that path is generally painful, and an error-prone process.
- There is a very long and difficult (marketing) path from product to money. Marketing and sales are two difficult jobs, where academics are not (most of the time) very gifted. Moreover, it may be hard to convince good marketers or salespeople to go with you in your adventure.
- Not all academics want more money. If my purpose was to earn more money, I would have originally chosen an other job. As a friend of mine say, if you want to be rich with high probability, start a pizzeria, then another one, then another one, ...