You will go through levels 1-50 doing your own alliance zones, and Cold Harbour. Once you complete the main quest (around the time you will most likely hit Veteran Rank 1) you will receive a quest to go to a different alliance (Aldmeri Dominion in your case). You will then quest through one of the other factions zone (Aldmeri Dominion). All the quests will be the same as the person who started in that alliance, but you will be in a veteran version of it (so you will not be interacting with AD players, all players will be from your own faction, all the mobs will be veteran level). Once you finish all the zones main story quests there, you will get a quest to send you to the other faction (Ebonheart Pact).

So.. in the end you do all the factions on one character