In order to acquire an egg of a Farfetch'd, you must have a male and female Farfetch'd in the same party at the same time, and then do battle with them. The egg spawns randomly.
Develop the egg by using it to give specific moves to its parents. Both parents must know the moves they receive from the egg. The parents can then adopt the developed egg as if it were their own.
With constant nurture and attention, the egg eventually hatches into a full-grown Farfetch'd.