I live in a one-bedroom apartment in Brooklyn. I have made a coffee table, four picture frames, a small bookshelf and two cutting boards in the last three years. I do not own a table saw or a workshop. Apartment woodworking is a specific discipline and I want to make the case for it here, because most articles about woodworking assume a garage that most Americans in cities do not have.
The key move: hand tools only. A Japanese pull saw, a good block plane, a set of chisels, a coping saw, a mallet. No powered anything. Hand tools produce less sawdust, less noise, and force you to work slowly enough that the mistakes stay small. Yes, it takes six times as long as a table saw. That is a feature, not a bug. My coffee table took a month of weekends. I still use it every day and it is more mine than any furniture I have ever bought.
Finishing happens in the bathroom. I put a cheap plastic tarp in the bathtub, wax the piece with a soft cloth, wipe it down. The tub is the biggest flat surface in my apartment and it drains. That is my finishing station. The neighbours have never complained because I run the saw only during the day and there are no loud tools. Woodwork does not need a shop. It needs patience and a specific willingness to buy tools slowly.