How can one determine the radical for a given character?
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/