This is a list of ways to get ideas flowing when trying to solve a problem, particularly in a team, based on Jerry Weinberg's Becoming a Technical Leader. Each of his ideas is great on its own, and they work well together, but there are also subtleties that you should be aware of.
Contribute a clever idea to the team. When it works, and when it's really novel, this is really cool. Most of the time, there are no new ideas, but re-hashed ideas from other sources. Instead of trying to get the perfect solution right away, spend your energy creating an environment where ideas can be exchanged and the "right" ideas can be recognized when they come along.
Encourage copying of useful ideas. Look for inspiration in your own branch, or in another knowledge area as well. And remember problems that you've already solved, in case this problem is similar.
Elaborate on an idea that a teammate contributed. Iterate, and make it better. Keep following through. Follow up the inspiration with enough perspiration to see it through.
Drop one's own idea in favor of an idea the team wants to develop. Strike a balance between stubbornly holding on to your ideas, and letting go of your ideas just for the sake of keeping the group happy and moving along.
Refuse to let an idea drop until everyone understands it. Like the previous example; this will come with time and experience.
Resist time pressure, and take the time to listen when other people explain their ideas. Take extra care to know why an idea is being dropped.
Test ideas contributed by other people.Look for the initial idea anywhere and everywhere, and then make it better.
Withhold quick criticism of teammates' ideas, in order to keep the ideas flowing.This is particularly important at the beginning, such as in a brainstorming session. Make the tradeoff to accept more ideas, which will be dropped later, than to drop early and not generate enough ideas. This improves with experience.
When you must criticize an idea, make clear that you are criticizing the idea, not the person who offered the idea.In addition to maintaining a good relationship with your teammates, this let's you explain which parts of the idea work, and which ones don't. It also let's your teammates in on how you come to your conclusions.
Test your own ideas before offering them.Take the extra time to scrutinize your ideas the same way you would the ideas of your teammates.
When time and labor are running short, stop working on new ideas and just pitch in.
Encourage the team to drop ideas that had succeeded earlier, but cannot be extended to the new situation. Make sure that the ideas fit in with what you are trying to accomplish.
Revive a dropped idea later, when it has value for another part of the problem. Remember your old ideas and solutions, because they may become useful again.