As a 4e heretic, I will make something different than what has been wisely proposed here.
So, each dragon has 4 "forms" : young, adult, old, venerable. Great.
1) I won't tell anything to the players about their characters being dragons (the last dragons alive, precisely...). There maybe some kind of obscure foreshadowing ("why are those guys trying to kill/capture us ? we have not done anything wrong !"), but both the players and the characters would remains ignorants of the fact.
Then, when they are roughly level 3 or so, I corner them into a desperate situation like an un-winable fight or being prisoners soon to be sacrificed by someone who wants to take their power. I then choose the PC who has have the least exposition time, the one who seemed the least efficient/powerful/optimised. I make sure he is the first "victim" to fall unconscious and dying. And while the other PC are busy keeping themselves alive (let's say there is a cave-in that let them think a few minutes about how to escape, while their enemies and their fallen comrade are on the other side), I talk to the other player, alone, explaining him that, while unconscious, he has a strange feeling of anger and power. Maybe he can discover and talk to his inner dragon, who will be very unhappy about the situation. I then hand him the stats of "his" new form : a young dragon, that is a level 3 or solo brute (if white dragon, I don't care about alignment, they don't exist anyway). I explain him that he will awaken himself in this state, but ask him to wait for my signal.
Then, I go back to the rest of the group. They probably have imagined a cunning plan. Or not. Anyway, the odds are against them, the enemy is close to defeat them... they can already see the body of their comrade, chained against the wall and looking barely alive. And when I think the time is right, I describe a sudden explosion, a hurricane of freezing cold, and I describe the apparition of the white dragon, a species that was supposed to be extinct for centuries. And I say the other player "enjoy yourself" while he probably crush the bad guys in a few round of awesome crushing power.
When he finish his job, he reverts to his human form, and fall unconscious on the ground. Now, the PC will have to find what happened (1). They will have to find that each of them is a dragon in human form (2). They will have to find what kind of dragon each of them is (3). And they will have to find how to control their power (4 and last part of the campaign).
I make each of them a different kind of dragon, who will need a very different kind of stuff to master his true form. I change their "true form" as they level up, but I make sure that, until they are able to master the transformation, the "true form" is far, far more powerful than their human shell. Damn ! We are talking about draconic might ! This is supposed to be overwhelmingly powerful and marvellous. I want the player to say "whoa !" each time a new transformation happens.
It's not bad to have one of the player take ALL the spotlight from time to time, provided it's not always the same player, and that each of them has his moment of glory.
At high level, when they are ALL able to master their draconic form, I will have to adjust them so that they are of roughly equal power. But for the rest of the campaign, I don't care, because I chose when they can transform.
The two forms are totally distinct ; they don't share the same hit-dice (wounding one does not wound the other), and they don't benefit from each other magic items. Those are really two different characters, rolled in one. The only trick is that one of them is not often present...