I live in an apt. I just started doing AG, I'm now on my fifth batch.
My kitchen is as small as anyones. or smaller... I have to clean before I brew and make sure I won't have people walking in and out as the front door opens into the kitchen.
I boil a five gallon batch in two pots. One 4 and one 5 gallon. I cool in my sink with an immersion chiller. (but I'm looking into no-chill)
I use my bathtub. I place my buckets in the tub and fill the buckets with water so I can sanitize my stuff.
My grains go down the garbage disposal. slowly.. Or I put them in bags and throw them out. I supposed you could put some down the toilet....?
I ferment in a closet. All my beer stuff (bottles, buckets, carboys, ect) live in the closet. Before my girlfriends son moved out, (it's his closet) I kept everything in the corner of the living room. Not all roomates/wifes/etc are as cool as mine is though.
Hose adapter for your sink you can find at a hardware store.
I made my wort chiller from copper tubing I got from HomeDepot. It was already bent into a circle, I just spread it apart and added hose ends.
The best thing to do for small space brewing is to evaluate what you need and be organized.