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When you get close to the house, a little boy named Timmy will run up to you and tell you that robbers have invaded his house and are holding his parents captive. If you want to save the parents, then you'll have to sneak into the house and free them before confronting the robbers. Otherwise the robbers will immediately execute the parents and you'll botch the quest.
If you can rescue the parents, then you'll receive 50,000 experience and 2 reputation points when you meet up with them at the Archer's Guild. They'll also give you permission to loot the house, but you'll probably have done that already anyway.
1 - Front Door
Don't go through this door until you've rescued the parents.
2 - Kitchen Door
It starts out locked, but you can find the key (#2a) right next to it. (Press the alt key to see the key and the outline of the door.)
3 - Bedroom Door
It starts out locked, but you can find the key (#3a) in the kitchen. Once you've opened the door and gone inside, the parents will automatically leave the house and go to the Archer's Guild.
4 - Inside Kitchen Door
It starts out locked, but you can find the key (#4a) in the bedroom.
5 - Inside Bedroom Door
It starts out locked (do you sense the trend yet?), but you'll find the key on Raven (#6) after you've killed him.
6 - Bandits
The parents will indicate that you might be able to surprise the bandits if you approach them through the kitchen door (#4) rather than the front door (#1), but there isn't any difference between the two. Raven (level 25) is the main bandit, and when he dies he'll drop two keys. One opens the bedroom door (#5) and the other opens the nearby cabinet (#7).
7 - Cabinet
It starts out locked, but you'll find the key on Raven (#6) when he dies. The only thing you'll find inside is the key to the chest (#8).
8 - Chest
It starts out locked, but you'll find the key in the cabinet (#7) in the other room.