I enjoy learning. I enjoy thinking. I enjoy teaching. What I don't enjoy is arguing. In my experience, there are 3 main methods for creative thought: Debate, Discussion, Deliberation. The 3 D's.
Debate is an extremely good way of inspiring creative thought. By having someone refute your ideas, and you defend and refute theirs, you must think on your toes. There has been many an occasion where I've come upon sudden realisation because of having to point out flaws in a well constructed argument. On several occasions, this realisation was the flaws of my own arguments.
I don't like debate. It's easy to let emotions run high, and lose sight of what your point is. For example, I was once discussing how evolution works. I decided to use the bird as an example. By the end of my argument I was pointing out that radiometric dating was therefore justified. I remember little of my argument, only that afterwards I felt foolish.
My advice to debaters, whether formal, or just amongst friends, is keep your cool. In the heat of passion, your arguments may seem valid, but upon later reflection, they were off the mark.
Discussion of a topic, whether it be as important as the existence of God, or as silly as the theme to your next party, is a good way to figure things out. It doesn't work well for extremely outspoken people, as most will try to prove their idea correct, rather then try and adapt theirs in the light of others. This is not to say outspoken people shouldn't discuss their ideas, just that they should be careful when they do.
I enjoy discussion, it allows for me to add my 2 cents in such a way that it helps others learn. By listening to others explanations and examples, I can grasp ideas that were until then completely unintelligible. It was through discussion that I first came to understand the concept of Natural Selection. From the above example, I later tried again at using the bird to explain evolution to a christian, with the help of a friend. Questions I couldn't answer my friend did, and ones he couldn't answer I did. We both started with a very basic concept (mutation causes advantages change), but during the discussion we reasoned out a strong explanation.
My advice to those wanting to discuss, find others with an interest in the topic, and ask questions of one another. Or do like I did, and try to teach it to someone, even if they know it better then you, they may have some pointers.
Deliberation is basically thinking about a topic. This is a direct approach, and as such can help quickly, provided you have a rational mind, and can look at a topic objectively. It has a varying amount of success, because you either don't grasp a concept, or your not hindered by the flaws in others ideas. It is also the most difficult for those not used to thinking. I don't mean to sound cruel, but most people I've met are sheep. They just do like everyone else, and never think for themselves.
I LOVE deliberation. I constantly do it. At any given time, my head is trying to figure something out. Sometimes it's important (like the evolution of the butterfly), sometimes it's not (why'd my mate put on that skirt). Because of this, I usually have an answer to questions asked of me. Whether or not the answer is correct is based mostly on whether my original understanding was good. Creativity is a vital ingredient to the reasoning recipe. Lateral thinkers are adept at thinking creatively.
My advice for people trying to think of the answer is, realise that there may be more then one way towards the answer. Don't assume the first way you think of is right. If it isn't working, try a new approach. Above all, ENJOY IT! If you're getting stressed about it, relax, take a break and get back to it later, you may find that after a break, your mind is ready to find the answer.
I'm fairly sure that these three avenues of thought are the three main "kingdoms". Although, they could be lumped into personal and public deliberation. In any case, the 3 I've listed here shouldn't be used alone to solve a problem. Thinking privately about a debate you've had is a great way to prepare for next time. Discussing what you thought with friends and colleagues will further hone your ideas, until you have a solid understanding.
Until next time, Fui fides tantum in testimonium.