Sorry if I didn't make myself clear. First, I was thinking in terms of a municipal or local race, commission districts or wards or precincts. Still the principles also apply to state and US congressional races. The final product you want is a map filled with polygons, each of roughly the same population. These polygons are compact, that is, they don't go snaking around all over the place picking up and avoiding certain areas.

The polygons need not be the same size (probably not, since population density is never uniform) but they must all enclose the same number of people. Second, you don't want regular polygons, rectangles or hexagons, because you don't want boundaries cutting through the middle of buildings and so on. You also want to be able to explain to the average voter where "district x" is with a simple map or verbal description. So you use easily locatable boundaries such as canals, street centerlines, or already familiar political boundaries like city limits and zip codes.etc. For example, a district description might include "all of zipcode 33333 south of 21st Ave and north of the river, plus the adjoining village of Cypress Lake Estates, except for the area east of 15th St".

The whole idea is not to produce a geometrically precise partition of the space, but to avoid favoring or cheating areas by deliberately designing complex boundaries calculated to do exactly that. And the citizen should be able to easily figure out his district by just consulting a sketch map in the newspaper.