Normally, you consider only a handful of options. Take advantage of computers to consider many more.
One problem-solving technique is to combine ideas from different places. It's common in science, for instance, for an algorithm or method developed for one problem to be applied to another - once someone's had the idea to do so. How can these combinations be made more systematic? Why not list all the useful things you know, generate a list of all possible combinations of them, and see which of these new combinations are useful and new?
Though this task would take a frustratingly long time if done manually, it's quick work for a program like the one in the image above (built with Elm. Check out the live demo, the code, or a simple python version of the core algorithm.
One way to apply this process is to generate business ideas. Just list your interests and skills, along with the markets you're part of and the business models you might use. Then you could list all combinations, or draw some sample from that group. If you have 10 interests, 10 skills, are part of 10 markets, and have 5 business models, then you've got an immediate 10 x 10 x 10 x 5 = 5,000 ideas to draw upon.
This sort of process applies in many circumstances. Want to create a new recipe? Maybe that involves choosing 3 ingredients from a list of 20. That leads to 20 x 19 x 18 = 6,830 combinations. Want to hold a party, but not sure what music to play, what to eat, and what games to play? List out your options. With 10 possibilities each for music, food, and games, you end up with 103 = 1,000 options.
If you're able to break a problem into distinct parts and think up a few ideas for each, then you'll always have plenty of ideas to work with.