How can one determine the radical for a given character? Many times, when reading Mandarin, I will happen across a character that I don't know. Usually, the radical along with some context will clue me into the meaning, but if I can't determine the radical, I'm stuck. Generally, I can spot many character's radicals, such as 氵, 辶 or 宀. However, there are characters who have one or more "radical-like" components to them, like 烋 or 想, and I'm unsure how to tell which is the true radical. Is there any general approaches which will at least more better than guessing? Are their certain radicals that generally take precedence over others when they both occur in the same character?

EDIT: My examples aren't the best, as both of those characters have radicals that are easy to pick out. A general strategy for when they aren't so easy is really what I'm after. For example, 能 seems to have two possible radicals, 厶 and 匕.
A rule of thumb is to look for the radical that seems to be more prominent. For those characters, it's pretty easy:


In 烋, notice how 灬 spans the entire character horizontally: it is the radical (火) 
Same thing applies to 想 : 心 is the radical.
As a bonus, in 强 which you have in your name, 弓 is the radical: notice how it spans the entire character vertically




The next best strategy is to identify and memorize common radicals and where they are commonly positioned, eg:


In 很 the radical is 彳. This is a radical that mostly appears on the left.
In 责  the radical is 贝. This is a radical that mostly appears on the bottom
In 军  the radical is 冖. When in doubt, pick the one on top (and/or the one with the fewest strokes).
In 明 the radical is 日. When in doubt, pick the one on the left.


A lot of this will come with practice.



There are some tools that will allow you to look up word and it will give you the radical, like this: 
http://mandarintools.com/