I encountered a problem in Unity but I am not sure where to start asking my questions.
I know that there are several channels in the Unity community, including the feedback forum, this answers forum, the discussion forum, the IRC channel #unity3d@freenode, and that Unity support can be contacted by mail (support@unity3d.com) or by reporting a bug or requesting support through the bug reporting tool.
Where should I start my search for questions about Unity?
There is no best place to get help. It all depends on the kind of question you have to ask, and the type of answer you need to get.
If you have a question that can be posed and answered in clear terms, you should probably ask on unity answers. Especially if you feel that answers to your question may be of help to other developpers.
If your question needs a lengthy description, and/or calls for a discussion rather than a definitive answer,you should start a topic on the forum.
If you need a quick answer on a basic question, you could check on the irc channel before posting on unity answers.
If the community was unable to help you, you should contact unity support.
These are only guidelines. In any case, there is no "wrong" place to ask your question, and you should not be afraid to. The different places in which you can get help are meant to ease your life as a unity dev, not to complicate it.
This answers forum should be the best place to start for several reasons, but mostly technical. It's the newest system and it facilitates even discussions, incetivating them to be small. It has big potential to be the next forum model, after some adjustments.
In practice Unity3D community isn't big enough so it's spread around. And we don't have an official starting point.
So my advise is to start on Answers if you think your question should have a direct answer and start on forums if you think it does not and you can't formulate your question in a simple or clear manner.
IRC is mostly for fans or if you are in desperate help and feeling lucky. On a small community it's hard to actually meet someone online at the same time.
My guess would be that if it's an apparent problem with the operation of the editor or the player, then you should contact Unity support. Anything else, such as a scripting question or the most effective way to accomplish something, would go in one of the other forums. Feedback is more for something that you don't really need or expect an answer to.
Unity Answers seems more like a place for "quick questions", or questions that are easily asked and have (reasonably) short answers.
How do you know if something has a short answer? That one, I don't know. :) Mortim's treatment of UA is probably better.