Here is how you can unlock Arvak, follow the video guide below to find the locations and how you can acquire it. What you will need to do in complete the side quest in soul Cairn. What you need to do is on your way to castle volkihar you need to stay in the path awhere you will come across a farantic soul calling for arvak. He will ask you to find him so he can stop running as the farantic soul was attacked an his Arvak was sent out by him. Below is the video guide on how to unlock Arvak.
Also take a look at the Skyrim Dawnguard walkthrough to help you complete the game.