You don't have to have a large vegetable garden, you can still grow a few things intermingled with flowers or in pots. Use seeds from the produce you buy i.e. peppers, tomatoes (although heirloom seeds are better). Most of the time, potatoes you buy from the grocery store don't sprout because they have been sprayed with a sprout inhibitor (the growers feel potatoes are not likely to be purchased if they are sprouting), but if you are fortunate to find one or two that are sprouting, cut them so that you have an eye (sprout) in each piece, let it dry out for a few days and plant in the garden. As long as the temperature/soil is over 40 degrees they should produce. Wait until after the potato plant flowers and begins to die off before harvesting.
More on growing potatoes here