In my experience, inspiration doesn’t feel like anything.  One moment I’m just thinking my normal thoughts and the next moment I have a complete solution in my head. 

Frequently it will be predicated by a completely unrelated chain of thought that somehow gives me a novel take on an existing problem I’m working.  It is usually pleasurable, especially if the problem was especially vexing.

Inspiration is the product of the combination of intent, will, desire, and ambition.  I have ambitions about a project, the desire and will to pursue it, and the intent to solve my problems.  I spend time working a project and when I hit a problem with no immediately obvious solution I’ll mull it over.  Most times I just work though it, but sometimes I get an inspiration.