I am not aware in the dream that "Hey, I'm dreaming!" but I am aware that my decisions will redirect the dream. The great thing about lucid dreaming is that it is a means of doing therapy on yourself. You are walking around in your own subconscious, after all. Things that you do there will stick with you after you wake up. For instance, with the standard-issue naked in public dream [http://www.dreammoods.com/cgibin/nakeddreams.pl?method=exact&header=dreamid&search=nakedintro], I decided to just deal with the issue in the dream head on.
"You're naked!"
"Yes, I am."
"What happened to your clothes?"
"I don't know, they just disappeared."
I refused to acknowledge that I had any reason for embarrassment and noted that it seemed to embarrass the other person, which gave me the upper hand as long as I kept my cool. So I carried on in the dream as though suddenly finding yourself walking around naked in public was nothing more than a minor inconvenience. After that, I became, for lack of a better term, more shame-resistant. I'd some how unlocked the ability to refuse to be embarrassed by circumstances beyond my control or aspects of my life that are just Who I Am. It was a really valuable gift.
There have been other things like that too. If I'm being chased by a monster or something, and I get killed, I wake up pissed off, go back to sleep, and have the exact same dream again and try different options. So really, I'm just replaying the level until beat the dream. It usually takes me three times, which is my usual in video games as well.