What does it mean by "one piece of furniture"? Does that just mean one piece of furniture that came with the house?
Yes.
There have been a few questions about what counts as a "way to make money," so I'm clarifying:
1. Any separately worded action. For example, if your Sim is a writer, you can "self-publish," "sell to publisher," or "sell to Literary Digest." In collecting, your Sim can "dig," "rummage in trash," "grab a poster," etc.
2. Any skill. Your Sim can make and sell a drink (mixology), catch a fish (fishing), etc.
3. Any career. Your Sim can change jobs as often as you want, but has to go through a full working day to count the salary.
4. Pop-ups. Sometimes your Sim will get money from a chance card at work, a Fame choice, winning a contest, etc. These all count. Check your notifications before deleting them.
5. You may also sell one item from personal inventory (a second fish you caught, for example), and one career reward, one party reward, and one additional item from household inventory. You may sell one piece of furniture that came with your house.
Note: Your Sim may sell many more items to raise the household income number, but count the method only once.