Gene,
In what sense are you meaning homesteading? Self-sufficiency, I'm guessing.
There are a great many things you can do in your tiny apartment. Do you have a balcony? You can start a small garden - tomatos, herbs, lettuces, etc. There's lots of resources for "container gardening".
You can also begin stocking up a food supply - each trip to the market, buy an extra flour, sugar, canned veggies, rice - whatever your food budget will allow. After a few market trips, you should have a small supply to last through a short-term emergency. Don't forget to include a first aid kit, peroxide, isopropyl alcohol, medications, etc....
Water storage - either by cases of bottled water or by saving/cleaning 2-liter bottles and refilling. If you are thinking your municipal water supply may become contaminated, there are some great home purifiers available. Right now, "Big Berkey" comes to mind, but there are others.
Where to store all this stuff in a tiny apartment? Under beds, behind sofas against walls, stack 2-3 cases of water and throw a table cloth over it - instant end table.
I hope this was the kind of info you were looking for.
Net