To view someone else's profile, I can click them and select "View Dota 2 Profile". My own profile doesn't show up in my friend's list though so I can't find a way to view it. I've tried clicking my avatar up above that, but it doesn't seem to do anything. Is there a way to view my own?
Click your name in the upper right. That's it.
Alternatively, use http://dotabuff.com/ to find your profile and view your recent games. It's a very useful site.