Both faction quests start with you finding the Dawnguard. To do this, head to Riften and talk to a guard there to find out that the Dawnguard is setting up shop nearby. The waypoint that you are then given is a little confusing. On the map, you'll be given the marker for the Overworld location of the fort but you can't get there directly. On the compass will be the marker for a cave that leads to the fort. Follow the marker on your compass to an area North of Riften.
When you find the cave, you merely need to enter and you'll enter the Dayspring Canyon where Fort Dawnguard is. When you get there, just make your way up the path to Fort Dawnguard and feel free to talk to the various people on the path. Make your way into the fort and talk to Isran about joining. He'll immediately sign you up and send you on a mission to figure out what the Vampires are doing in a ruin out by Dawnstar