Most birds follow the same technique whether on land or water, domestic or wild, because that is the way they are tuned (few birds actually mate in the air while flying).
After breed specific courting rituals, the male will "mount" the female... they usually grab some neck feathers of the female "pinning" her, then clamber on to her back. Some will tread with the feet and wag the tail with fervor. The willing female goes submissive and moves her tail to the side to allow easier access. The hen will do a bit of body twist, but how the male attains penetration was always beyond my line of sight. It is a very brief connection in actuallity, and though awkward and regularly comical, it is effective.
The avian male organ is a thin, fleshy, corkscrew that is normally carried up in a body cavity just inside the cloaca until used. Sometimes after mating it will hang in the breeze momentarily until retracted.
The cloaca is the orifice that all birds share (and close cousins such as reptiles). It is the waste vent, genital orifice, and egg exit (birth canal), all in one.
Waterfowl do not have to leave the water to mate and favor it, though they will also mate on land. Ground birds such as chickens prefer solid footing. "Tree birds" will occasionally lose their grip and "free fall" off of their perches while still mating and then continue to fly.
Chickens are not monogamous and the ratio of males to females can be up to 1:20. Ducks 1:5. (servicable breeding for farm utility). Geese are monogamous and mate for life, though they have occasionally been induced to accept another mate after mourning and a lengthy separation. Pigeons are monogamous until their mate is absent for a breeding cycle (30 days) or two.
If you do a search for "hatcheries" or particular chicken breeds, you may find useful links. I have yet to find any that actually explains the physical act of breeding.
This information comes from my personal experience and acquired education. I had a farmstead where I raised chickens, ducks, and geese among other things. I am soon to embark on raising Modena and King Show Pigeons and so have done my research into their husbandry.
I hope you find this informative, but must leave it to you to find your own useful links for reference.
ADDED: For the curious: The eggs we eat are not fertilized because they are mostly commercially produced by hens in batteries of cages and tended production line style. Efficiency = profit, hence the outcry for the inhumane husbandry of the majority of our animal food products. A fertilized egg may also have "unappetizing" spots and blood clots (which occasionally appear from a spent bird also), so these are separated out. Eggs are "candled" to see inside the shell and those with inclusions go to manufactured egg products.
Some eggs fresh from a "Family farm" may very well be fertilized since most allow their rooster(s) to intermingle with the hens due to the need to produce progeny (chicks) to sustain the flock. However, in some operations, breeding is usually planned and the "broody hens" are separated into their own pens so as not to use fertilized eggs for food.
Once a production hen's egg output declines to inefficiency or she proves to be a poor layer, she becomes food. Most "chickens" in the market are actually young roosters and spent hens.
College Animal Husbandry coursework