I don't know about most entrepreneurs, but here are some ways I've personally observed in fellow entrepreneurs:
1. Innovation: Talented technical specialists come up with a cool, innovative technology as part of their work/research, and decide to implement it, produce it, and sell it. The chances of commercial success are small, because using a product just for the sake of technological novelty can become a short-lived fad at best. But, a cool, innovative technology can be patented and sold as is to the industry - a small, but respectable exit. A couple of my friends became millionaires this way.
2. Cloning an existing idea. About 5 years ago 3 young guys returned from a trip to US and created a Groupon clone in their country because they liked the idea (Groupon was much more popular back then). They did it quickly and with a very small budget too. 10 months later Groupon decided to expand to that country and instead of trying to compete with these guys they just bought them out for $10-15M to get their hands on the existing customer network. That's $3-5M apiece. But you'd have to be in the right place at the right time and more often than not the big company may sue you for infringement rather than buy you out.
3. Automation: A highly qualified service provider, an undisputed authority in his/her field, suddenly realizes that this service, which has never been scalable, can be made scalable, usually by automating it partially or completely. One famous example - Uber. Also, that's the startup I'm in right now. We're building a software suit that replaces advisers (lawyers) in the field of export control regulations - it's more reliable, faster, and cheaper than hiring an adviser. Statistics says that this method has perhaps the highest success chances. But to succeed, you'd have to have the deepest understanding in the field (or be very very lucky).
4. Pain-centric: Starting with a problem. Look around you, think of the most significant pain you, or people around you, encounter in everyday life or in some specific situations. Then figure out how to solve this problem in a scalable way. Try many approaches, one by one, until you find something that works. Don't get fixed on some idea or principle, like "it has to be a mobile app" (no it doesn't - it can be many things). A friend of mine has a grandfather who forgets to take his medications, so he built a reminder app. This app now has millions of devoted users, it's profitable, and there was an acquisition offer for like $20M (which was declined). I believe that this is the best, and the most appropriate way of looking for ideas.