I was just pondering this little thought... How does your character find out he is the last dragon born? Does he get out of the prison (like all the other TES games) and think, "Hey, i think I can shout at dragons!" I was thinking a little along the lines that maybe an older man guides you through your journey, and tells you that he was the thought to be last dragon born, until your character. He tells you and guides you through abilities of a dragon born and such.

This is probably very unlikely, but its something to think about.

Esbern supposedly tells you that your a dragonborn and something will probably happen with a dragon shortly after escaping that you will unlock your first dragonshout from.

I'm pretty sure the way your character finds out he is dragonborn is connected to the Riverwood dragon claw quest which is depicted in the developers demo. That's where the first "word wall" is found....I read somewhere (I think the GI article) that's where you realize your dragonborn-ness.

Okay, that makes sense.

Unlikely. Todd already knew Unrelenting Force, which is probably your first shout, before he found that word wall.

I'm in agreement with Sleign.

He could have been buffed for the demo.

Todd picked up a second shout in Bleak Falls though and then he fought the dragon after he cleared the dungeon. How was he able to get that second shout?

This. Anything is possible in a demo. Todd could've had all dragonshouts unlocked in the demo for all we know.

you probably just think you can use the Thu'um normally until you meet the greybeards and realize your already better at it than them.

It occur's to you that you may be different with an ethyreal being saves you from being executed at the beginning of the game. (Something like that states by Todd himself)

Most likely, Esbern intervenes in some epic fashion and rescues you at your execution, guides you to some old temple and teaches you your destiny.

He probably sends you to Riverwood, which is the place that you find the quest that gives you the first mention of a dragon shout.

It's already confirmed that you find out you're dragonborn at an event that has a dragon involved. (I believe that when you absorb the soul of your first, scripted dragon.) Then, the Greybeards call out your name, "Dovahkiin.." and you make your ways towards them