I found that the easiest way to obtain levels was to take my Auriel's bow and block off the sun, then turn into a vampire lord and start sucking the life out of people.
I mainly went into towns and imperial soldier camps, but I also roamed a few forests. Every non-quest related NPC that you kill will give you a bit of that sweet experience you're looking for. I also suggest taking the "Detect all creatures" ability first, just so that you don't miss anything. Animals don't appear as red dots on the screen, but they give you life force when you drain their life force.
EDIT: Make that some animals. Foxes and chickens don't give exp, so I suppose only larger animals (i.e elk, bears, horse) will give you exp.
EDIT2: To make it even clearer, just re-do step 4 & 5 for some time:
1. Turn into a vampire lord (In your powers menu if I remember correctly)
2. Start floating (Press LS by default, your sneak button.)
3. Hold your right trigger down and charge the life drain spell
4. Cast it on an enemy (Guard, villager, bandit, elk, saber cat, gargoyle etc.)
5. Kill the enemy with it. You'll get a notification for this in the upper left corner of your screen.
EDIT3: SeraphimNeeded mentioned a few core tips, thanks!
* If you are a werewolf going into this or want to be able to become one later, you will be able to switch back and forth by talking to the correct people from each faction
(These being Aela the Huntress and Serena. To get rid of vampirism you can go to a pub and ask for the latest news. The barmaid will tell you that there's some weird guy in Morthal that touches vampires.)
* While playing as a vampire, Lord quality or not, you may want to consider The Lady guardian stone (Located directly west of the Guardian stones, on a small island in the middle of a lake) and the Recovery perk from the Restoration skill tree (requires skill level of 30, plus prereq perk). Together, those increase your recharge rate on health, stamina, and magicka, overcoming the Weakness to Sunlight's disabling of recovery.
* If you have the Summon Gargoyle ability unlocked, you can summon it and drain its soul. You can double this if you have the Amulet of the Gargoyle.
EDIT4: Many people (So far including SeraphimNeeded, Slider257 and enjibenji89) have pointed out that you can turn into a vampire even though you side with the Dawnguard. To do so simply talk to Serena in the fortress. PLEASE NOTE THAT IF YOU CONVINCE SERENA INTO TURNING HERSELF INTO A HUMAN YOU WON'T BE ABLE TO BECOME A VAMPIRE LORD IN THAT SAVE ANYMORE. Be cautious.
EDIT5: M0KKAN (Thanks!) pointed out that your drain life spell is weaker when Serena is following you, be sure to tell her off before embarking on your mission of misery!
Holygrail311 informed me of the importance of being hungry: your drain life -spell works better while you are starving! This might help you level up your vampire side amidst the actual gameplay, just kill a few people when ever you are hungry!
Yet to be confirmed (will do so in the coming days) is a tip by Come on and try, who said that if you equip two (2!) Daedric swords and turn into a Vampire lord and back you'll have the Drain life spell in your right hand when you turn back into your human form!
This could prove quite useful if you don't wish to float around in a form of a rat!
And lastly, if you're really going to give me a negative vote you should atleast give the reason for it.
Edits on 11.4.2013:
-Removed a seemingly hurtful word
-Fixed a few random things (Having to side with vampires not being necessary etc.)
-Added edit 5 with a few more tips
-Bolded the names of the authors of additions