I've been using chickens in the garden (and for many other things) for about twenty years. I manage a hectare plot of ornamental gardens, a food forest and about 3000m² of vegetable gardens and I couldn't do that without the chickens and other poultry. We have about 50 chickens, a dozen or so ducks and some turkeys.
I'm sure I've posted in Permies before about this but I'll repeat it here. Observation is the key, watch what the chickens do and think how you can use that to your advantage (and theirs!). Go slowly and try new methods using all the the permaculture principles.
Jeanine has made some very valuable points but bear in mind that each garden is different, different breeds of chickens and even individual chickens are different.The main thing to consider is that you can't do this in a small garden, the chickens will destroy it and break your heart.
Our chickens are completely free-range and I use a lot of different strategies to protect my plants. Covering them with cages, using moveable cages, using very dense planting and the judicious use of sticks around plants.
There are over a hundred photos in one of my sets in this link, which show the techniques I use, the vegetables and so on that I produce and the overall results of my designs.
This is one example of a "before and after" shot. The chickens clean the paths and the beds to allow the spring sun to heat the dark earth and they also eat overwintering insects. I plant, with a few sticks around each plant to protect them, then heavily mulch the bed. The chicken manure helps to compensate for the straw's nitrogen robbery and keeps the earth warm to help the plants become established.
Once they've finished working, they go elsewhere - wherever I've disturbed the soil, turned over a bed of manure or cleaned out a goatshed. This photo is taken a few weeks later.
The crop here was exceptional.
Here's the link : https://www.flickr.com/photos/hardworkinghippy/albums/72157615288270606/with/1095672797/