At this point you need to depart on your new quest to help her reach home -- but instead of backtracking the way that you came to get to the outside, use the path that is on the opposite side from the one you entered by when you arrived here. On the way you will find that the tomb was built with its own special defenses, and clearly someone does not want this particular vampire wench leaving without first putting up an effort to stop her! After you defeat the Gargoyles and then go up the dirt ramp to the right and through the door, which will lead you to another crypt area.
After you defeat the Draugr that spawn when you pull the lever at the top of the stairs, look around and you will pass down a hall into what looks like an arena, and have some more battles. If you look around this area (and you brought a pick) there are some Malachite Ore Veins -- seriously if you have the pick why not? There are four veins here just so you know.
As you explore the area you will discover a Word Wall from which you learn the first word of power for the Shout Drain Vitality -- you may as well activate that now, you should have plenty of Dragon Souls.
Remember to loot the chests here and, when you feel like you have everything that you want, continue on to the exit door and back to Skyrim.
-- The Shout Drain Vitality --
You have learned the first word to the Shout but there are two other words that you need to learn in order to complete it. The first of those can be found in The Forgotten Vale, and the second in Arcwind Point. While The Forgotten Vale can only be accessed during the upcoming quest Touching the Sky, the wall at Arcwind Point is accessible now.
To reach it, fast travel to Haemar's Shame in the mountains near Ivarstead (to the southwest), and then follow the path south until you see the icon (a black temple outline) on your compass (assuming you have never been here before) and, when you see a medium-sloping wide area of snow to the south head up it to reach Arcwind Point.
Unlocking the Second Word of Drain Vitality
When I arrived in addition to having to battle some Dragon Priests I had to battle a Legendary Dragon -- and once they were managed, the word wall is found to the right of the shrine up some steps. Simply head up and absorb the second word in the shout, which basically gets this out of the way -- yeah, I know, getting things out of the way is not what you usually think of in playing but there you have it.
With the second word to the shout known you will pick up the third word, thus mastering this shout, during an upcoming quest -- the reason that we did this now is simply that having this Shout at full power will come in handy later in our adventures!
Note: this is NOT the Shout that is referenced in the Achievement for learning all three words of a shout -- that one is part of the quests.
-- Stage 2: Heading Home --
You are a long way from Serana's home but of course you can fast travel, so pick one of the locations nearby that you have already revealed -- either Rimrock Burrow or Pinefrost Tower -- and head there now. Once you arrive you can go the rest of the way on foot, at which point you will now be approaching the point where you have to make a choice as far as factions go -- so you may want to make a save before you enter the castle -- actually you really should make a save and note down the time so you know which one to come back to for your permanent play-through.
When you arrive at the castle Serana stops you to fill you in on a few facts -- and after that you will notice two basic situations -- some of the people here are happy to see her, and while her father -- Lord Harkon -- appears happy to see her sort of, he also appears to be more happy to see the Elder Scroll that she possesses...
The situation quickly focuses upon you -- as Harkon begins asking her questions about you, and his daughter reveals that it was you who rescued her, to which her father basically offers you a reward for that service -- you can either become a Vampire Lord and join their faction, or just this once he will let you live, and you will be allowed to leave un-punctured and still in the form that you arrived in.
This is where you have a tough decision to make -- and hopefully you took my advice earlier and made a save that you can come back to later. If you do not care about playing through both faction stories just pick the side you want to play through on. If you do care about being able to experience both stories, your best approach here (assuming you made the save earlier -- if not save NOW) is to pick the path you actually do not want to have as the one you will complete the expansion under, so you can play through that, and then once you have experienced the story revert to the save and play through on the side you actually want to complete the expansion with.
For me the choice was obvious -- while it may be fun to be a vampire for a little while, I am a hero at heart, so siding with the Dawnguard is the way I prefer to go -- and that means that I picked the Vampire side at my first meeting with Harkon so I can experience that before getting through my "real" play-through. YMMV but once you make your choice, simply jump to the next section that applies.