I want to put off the main quest for a while. I've defeated the first scripted dragon and i'm just going to see the greybeards now. I did some of the bard quests and i haven't seen any other dragons.

At what point do they start appearing?

Immediately though rare until further in main quest.

once you're done with the greybeards I think they will start appearing.

They start appearing when you least suspect it.

I stumbled out of a tavern, drunk, poisoned from tasting ingredients, and in my clothes instead of armor and a dragon swooped from the sky and started tearing the village a new one. Not my finest moment, since I ran back inside and ordered another drink.

I haven't seen the greybeards yet, but I've already been attacked by two dragons in addition the the very first one.

I have yet to go to see the greybeards, but I did kill the first dragon on the main quest. So you don't need to meet the greybeards for dragons to start appearing.

After that I've encountered three in my about 12 hours of playing. Two at word walls which I don't think were random. There was also a boss-like draugr who used dragonshouts and had insane amount of health. But the dragon was the one to kill it, haha.

And one in the mountains while just randomly running around.

I've hit level 5 and just finished Bleak Falls Barrow and haven't seen a dragon yet. It took nine hours to get that far but I can't see anymore so it's bedtime....goodnight all. I wish I didn't have to stop playing though.

Yeah I been running into them up in the mountains so watch out if your going through them. Also you'll see a dragon head on your compass if you get close to one just a heads up.