How do I obtain the ebony blade and how do I power it up?

Solution 1:

The Ebony Blade is the reward for the Daedric quest The Whispering Door. You can begin the quest once you reach level 20 and:

You defeated the dragon terrorizing Whiterun early in the main questline.

To start the quest, ask the innkeeper in Whiterun about any rumors he might've heard.

The Ebony Blade is a most sinister weapon. Its description says:

Strengthened by the blood of deceit.

To do that:

You must kill the people who you've befriended/done favors for in the ultimate act of betrayal. Every 2 kills increases its life leach .

Solution 2:

I obtained mine by inspecting Jarl Balgruuf's children (Look at inns or ask people for rumors of his children being "weird") Then you go to talk to his son, which then speaks of the "Whispering Door". Once that happens, you'll have to aquire the key either by killing or pickpocketing the Court Wizard or the Jarl himself. Unlock the door, then the Ebony Blade is there.