I would say a few at the most, not sure on how accurate that is though, I try to save the main quest line for last, I've only done a handful of main quests and I see dragons all over the place.
The game will guide you to Whiterun (though you don't have to go). Once you talk the Jarl, you'll be given a quest. Completing that quest will activate the dragons.
Helgen -> Riverwood -> Winterrun -> High Hrothgar -> Radiant Dunguen Run -> Riverwood -> Kynesgrove
Sorry they start spawning long before Kynesgrove quest. They start spawning like mad cliff racers after the first dragon near Whiterun and you become thane.