How does the human body think?

This is a question i don't think anyone can really answer with any certainty.

The way I look at it is..
Your brain is made form billions of neurones and trillions of synapses (connections).
I think that when you have many many simple things, they can make something very complex, just how pixels can make a complex image.

So the neurones form paths, that allow us to process (but not necessarily think).
E.g. I'm currently listening to music which is making me relaxed (missing out the complex physiology of how sound if processed). I believe it would go something like this.
Good-music stimulates neurone like this (|_||_|__|||_|) -->match to another neurone with that firing rate, which is associated with good music-->makes me happy(release endorphins).
Bad-music stimulates neurone like this (|_|_|_||||_|___)-->match to another neurone with that firing rate, associated with bad music-->stimulates neurones associated with distaste.

obviously this is just an example, and which neurone is programmed with those particular firing frequencies depends on previous experience (have i heard the song before, is it associated with a good experience etc.)  

So then to think, you require processing. On a synaptic scale this is where multiple neurones can modulate a synapse.
So back to the example, if i'm relaxed, i might not like to listen to some heavy rock. So the neurone that matches that firing frequency may be inhibited by another neurone associated with relaxation.
Giving me the 'i'm not in the mood for that' feeling.

I personally believe that if you have enough of these complex processes occurring at the same time; then you get a self-aware being, with empathy and emotion.

What i have trouble explaining is what awareness is (which is probably what you wanted explaining).
I believe this comes from curiosity, which has evolved (because it is a good trait).