Lord Harkon presents you with two choices:

I will accept your gift and become a vampire
I don't want to become a vampire, I refuse your gift

Choose the first option if you wish to become a Vampire Lord. Harkon asks you to be still, and bites you. You lose consciousness and wake up in a strange chamber. There is a fountain of blood in the center of the room.

Lord Harkon: Awake at last, good. The power is growing within you, and now you must learn to wield it.

Your options are:
I'm ready to learn about my new powers
What happened? How did I get here?
What is this place?

If you ask him what happened, Harkon tells you that his blood is potent, and that at first the body is overwhelmed by it. After his bite, you collapsed and fell into a slumber. Now your flesh has acclimated to the new blood that courses through your veins. Harkon assures you that no harm was done, and in fact your strength surprises him. Not all mortals can withstand his embrace.

Tell him you are ready to learn your new powers. Harkon says that with his guidance, you will become a deadly instrument, striking terror in the hearts of mortals wherever you tread.

Your training begins. The true power of the ancient blood is found in the form of the Vampire Lord. Harkon instructs you to assume the mantle of the Vampire Lord before continuing.

Your objective is to use your Vampire Lord power.  Open your magic menu, go to "Powers" and locate the following power:

Vampire Lord
Transform into a Vampire Lord. Use the Revert Form power to change back.

Note:
To change back to a human, use the power REVERT FORM. If you cannot find Revert Form in you powers menu, go to your FAVORITES MENU and you can go back to becoming a human again from there.

Note that unlike a werewolf, you will be able to transform into a Vampire Lord and back at will.

In Vampire Lord form, you can drain the life from your foes with your right hand. With your left hand, you can wield the power of blood magic to raise the dead. You can also call upon the powers of night to turn into a swarm of bats and reappear some distance away. Should you run out of magicka, you can descent to the ground and fight as the beasts do.

Harkon tells you to land on the ground to continue. You are weaker on the ground, because you cannot access the blood magic. However, the night powers are still yours to command, and your claws are still formidable weapons.

You can switch between magic and melee modes by pressing the appropriate button.

Harkon tells you that over time, your power will grow in strength and you will find new ways to use your gifts. Note that even if you are at level 81 (the level cap), you will still be able to level up us a Vampire Lord by draining blood from enemies.