You need to find the ghost who owns Arvak in the Soul Cairn. He should be right along the path that most people take while there. He'll ask you to save Arvak from his fate in the Soul Cairn. To do that, follow your quest marker to his skull, which will be guarded by several Bonemen. Retrieve the skull, bring it back to the owner, and he'll teach you the "Summon Arvak" spell.
While on a quest in the Soul Cairn you'll be approached by a soul who talks about the horse. You find the horse's skull and return it to his master and he teaches you the spell. It's a conjuration spell, not a power, so it can be used whenever, but it costs magicka.
Taken from a livestream I was watching earlier. --- Play with guns and drink and cuss and tell your kids that drugs are fun.