General Information
There are several species, and subspecies, of partridges, from the Chukar, to the Rock, the Red, Gray, and many others. Typically they are native to Asia and have been introduced to other parts of the world as game but more and more people, or hobbiests, are keeping them as pets, or as ornamental birds. They live about 12 - 15 years, and both males and females look identical.

image sourceSelection and Purchase
Not all species or variations are available everywhere, as such you may have to settle for what ever is in your area to start. Chukar Partridges, as in the photograph, are generally considered one of the easiest to start with, although no Partridge is considered terribly difficult. You may find them at breeders, if you are unsure of one in your area, the local feed store might know of somebody. I often see them for sale at exotic livestock and bird auctions.
Males tend to be slightly larger, and have a slightly larger knob on the back of their legs. I suggest you purchase a "mated pair", or trio. If space allows, you can have more birds, as they do get along in smaller groups.
Look for healthy, active birds. If their legs are scaly this may indicate old age. Look for bright eyes. Also check the facilities, if they are neat, chances are their birds are healthy, if their place is a mess, chances are their birds are stressed or unhealthy, do not reward sloppy breeders by purchasing their animals. The cost will vary depending on availability and demand in your area. Plan on transporting them home in a pet carrier or cardboard box.
Feeding
Partridges eat seeds, greens, and insects. You can feed them a "game bird" diet, or even chicken feed, as long as they also have access to grass, and can forage for bugs. Additionally they should have smaller grit, and even oyster shell if you are breeding. A shallow bowl should be used for water, or a proper chicken waterer.
Housing and Care
Partridges require a minimum of six square feet per bird, although more is certainly ideal. I recommend at least 36 square feet for a pair. They need their ground to be dry, or at least, not soggy, so a higher elevation is good, as well, the addition of some rocks or tree stumps is important. Like all animals, they must have some shelter from poor weather. This can even be a dog house, or old shed, anything that provides shade, protection from rain, snow, and wind. I suggest putting cardboard on the floor and covering it with straw. If possible provide a "upper level", this will not be used as much but actually increases the room within the shelter should they need it.
Although I have referred to keeping them as pets, they are not typically a pet you can pick up and hold to play with, they will tolerate handling, but are not an animal that appreciates it like a cat or dog would.
Partridges are compatible with other birds, and are often kept with doves, or even Bantam chickens. It is best to keep them with other gentle birds around the same size, if you are going to keep them with any other bird.
Should you get some laying fertile eggs, you may want to remove the eggs and have a broody hen raise them or you should put them in an incubator. Partridges may lay 40 eggs in a summer, but getting them to sit on their eggs to hatch them is a tricky matter.
Other Information
In many places it is legal to let them go into the wild, in other places it is not, make sure you check before releasing any domesticated animal into the wild.
One advantage of keeping Partridges is that they provide insect control.