How do I go about being able to purchase this house?

Well if you did the optional dark brotherhood quest and killed the woman in Windhelm it's bugged and you can't otherwise you have to do "Blood on the ice".

If you picked imperials you wont be able to buy it as you cannont become thane of that hold
I found that out the hard way.

If you really want it you can use the console to setstage and have the house i dont remember what the exact command is but it is possible even though your chose
Imperials over stormcloaks

really, u can't? :/ Not even when u finish the imperial campaign and an imperial supporter becomes Jarl there? I played stormcloaks, but a friend of mine played imperial and could as soon as the new jarl was in place..

Can you get the house if you take over the city. I was planning on going Imperial...

There is one quest that purchasing the house depends on and, alas, I am one of the unlucky ones because I cannot get the quest to start. "Blood on thin ice" is the quest you need to complete if you can get it to start. Without this quest you cannot buy the house.

Wainting for patch 1.2 sadly.

How do you start blood on the ice?

Go to the graveyard on the western side in the city. Talk to the guard standing over a dead woman..

The strat guide says you have to enter Windhelm and leave ( when leaving you must also enter another city/town/dungeon/etc ) and then return 4 times. One completed enter the town at night and head to the graveyard and if its working you will come onto the scene of a murder. Talk to the guard and the quest starts.

Hope it works for you becuase it doesn't for me and not having the best house on my first play thorugh has been my biggest Skyrim let down. I only have few lose ends to tie up and one more achievment to earn and im done playthrough #1, sadly without the best house.

Thats not the case. I chose the imperials and became thane for the new jarl.

So do I need to do the Blood quest or can I just get the house by doing the Imperial quest?

Do the blood on the ice quest. However...this quest is extremely bugged. It seems alot of people can't even get the quest because the target you're supposed to kill for an early Dark brotherhood quest bugs the blood on the ice quest and it cannot be started. Plus...even when you do start/finish your home still has blood stains all over it.

You can still purchase the house if you join the imperials, you just have to finish the civil war.

I was able to buy the house as soon as i finished that for less than what the asking price was, i had 9k on me and i think he asks for 12k yet i was still able to buy it... Blood On the Ice quest started for me as soon as i entered the house.

And yeah the blood stains seem to stay forever which is rather annoying.

Oh Bethesda...

Im not sure the Dark Brotherhood affects it. I didn't join the DB before trying to buy the house. The Fire on Ice quest simply wont start.