Sorry to the two others, but their guides don't really tell you how to do this properly.
Firstly don't buy anything until you have 16000 coins, to save confusion...
Next play through the game until you are on level 6, then go back and complete the tiki challenges which unlock after you complete the levels.
This will allow you access to the kitchen and bathroom within his house.
Firstly go to the bedroom, purchase Gary's food bowl  and his bed (newspaper)  without leaving the room or you will never be able to get this achievement. Also in this room buy the two pictures [200x2] and Spongebob's bed .
Move into the bathroom, by opening the chains which should now be unlockable (if not you need to do more Tiki challenges). Purchase the waste backet , toilet , bathtub , towel rack , picture , mirror , dryer  and the duck sitting beside the bath .
Now go downstairs and enter the living room where you can buy the armchair , two pictures [200x2], a sofa  and the trophy table beside it .
Now open the kitchen, the natural progression will allow you to unlock the chains, buy the two cabinets on either side of the door [500x2], stove , fridge  and finally the sink .
All in all these purchases will cost you 16000 "happiness nuggets" or coins, and you will have the most tedious 30G you'll ever get... despite I'm sure purchasing Gary's bed and bowl at the same time it didn't unlock so had to play this crappy game again!
*If you have any complaints with this, please leave a comment instead of a negative vote and I'll update it!*