I'm afraid this won't be too comprehensive, but meh. And obviously if you want to discover how to move furniture on your own, don't read this!
Go to the Repository and you can move furniture! You'll have to select a piece from the Rukis first. Then go into the repository and click on the Neopet you see near the entrance. Then click on the button to talk to him and he'll tell you what level to place your furniture on. Then all you need is to find an unsmudged outline of the furniture piece you need (square is table, sort of square with two bumps on it is scroll rack, smaller rectangle is bench, circle is lamp). Get next to that outline and click on it, and you'll place your furniture! As of now you can work your way back to the entrance and leave and get as many furniture pieces as you like, one at a time. (If you click on the wrong piece you'll get thrown out for 30 minutes, I've heard.)
(I didn't mention other subtleties to the plot, like thieves stealing the furniture, but others can discuss that. I'm back to forcing my darling Lillaray into backbreaking labor. )
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