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.