And where is it?

breezehome, next to the Blacksmith, near the main gate. You need to be a Thane though, before you even get the opportunity to buy.

Sorry,what\s a Thane?

An honored warrior of the Jarl. You get the title / house by completing the main quest.

Thanks,I think that I am.

No you don't have to complete the main quest to become Thane and get the house. You just have to finish the quest that the Jarl gives you. He'll make you Thane, give you a weapon, then you can talk to the Steward and you'll have the option to buy Breezehome. A nice little house near the gate to Whiterun by the blacksmith shop called Warmaidens. The house costs 5000 gold plus a seperate amount for the decorations and furnishings. The house will run you about 6000-7000 all together. However, there is a quick simple way to get the house and furnishings for free without cheating or using console commands and it won't cause any harm to your game. If you're interested just message me since I might not look back at this thread.

I think that I did this quest as I thought that I was told that I could buy the house but I need the key?

Ya ,I am a Thane.Whom do I speak too,I need the key.Thanks

Is this a serious thread?

Why not ask the people in Dragonsreach, and find out for yourself. God knows how you'l survive when the real challenges happen...

You have to be a Thane in the town you want to buy an house. Being a Thane in Solitude wont help you to buy a house in Whiterun. However in Dragonsreach you have to speak with "Proventus Avenicci", he is the steward and he usually wears fine clother plus a two-handed weapon. Another sign of being a thane in Whiterun is, that you have a huscarl called Lydia by your side

By the way until the CK comes out I guess the Breezehome is the best house so far. Other houses may have some manequins but aren't that useful at all. You have several shops close to it, a forge and an alchemist. There are several close ranged chests where you can easily store things. In other houses like the one in Solitude you have to run from one room into another just to find another chest to store things...

You need to speak to the Steward in Dragonsreach. He's usually standing to the left of the Jarl when he's sitting in his throne. Speak to the Steward, and if you have been honored Thane of Whiterun, the option to buy the house will be available. If it's not available, you need to make sure you finish the Jarl's quest.

And Lydia will be your housecarl after being named Thane, but she will be sitting in Dragonreach until you speak to her and ask her to follow you. If you buy Breezehome, Lydia will go hang out in there until you need her. Same goes for every hold where a house is available and you're appointed a housecarl.

Give the steward in Dragonsreach 5000 septims to get the house. As far as I know there aren't any free houses in Skyrim. And then you have to pay for the upgrades.

No there aren't any free houses but there is a simple and quick way to not pay for the homes or furnishings when you go to buy them. Push the steward over near a storage container by sprinting into him. Sprinting into people causes them to stumble backwards. Say yes you would like to purchase either the house or furnishing and quickly exit out of the conversation and click over to the storage unit and unload all of your gold into the unit. The Steward takes a second to say something like "yes that's available and it will be there when you go into your new house" and this gives you time to back out of the conversation and dump your gold. Then grab your gold back out of the container and buy everything else you want by doing this over and over until your satisfied. It does indeed work because I bought both Breezehome in Whiterun and Proudspire Manor in Solitude doing this. If you have say 200 gold still in your inventory, they will take that for say a 1000 gold furnishing. I left a bit of gold in my inventory because I felt bad getting everything for free. I think Proudspire was over priced anyway.

You can get the archmage's quarters at the college for free, but you have to complete the mages quest line.

You can also get free sleeping quarters and a storage unit when you join the Companions in Whiterun.