We allow ours access to over an acre, but you can pasture birds in any backyard, so long as you arrange things appropriately. Chickens will scratch nearest to their "home". Any run you give them will be denuded of grass gradually from the coop or other building and then successively further away. This will happen no matter how big the run is, all the time there are enough chickens using it that they can scratch grass up faster than it can grow back. Some folk put straw down on this area to save the grass. I prefer to either move the run, or move the entire set up, depending on the size of the building.
We have two large and non-moveable sheds for our general laying flocks, which each have two 50' x 20' runs, that we alternate between by opening or closing access doors as required. Any standard garden shed would work for this set-up, an 8 x 12 shed will provide shelter and nests for 50 birds. You will need to provide roosting poles at several levels in a step arrangement. Ideally access to nestboxes should be possible without entering the shed.
For fewer birds, and total portability, coops and/or runs can be modular or complete, and as a general rule of thumb each hen needs a "home" two feet cubed, with a run 2 to 3 times that size attached to it. This size will actually accomodate 3 hens, a pair for mating, or a hen with chicks, provided it is moved regularly.
Any shape coop will work. Old cupboards make excellent coops, as do children's tents. The choice of deisgn, materials, and size must be based on your individual circumstances.
First consider their safety. Do you have dogs, or do neighbours dog or other large predators (wolves, coyotes, etc) enter your property? If so then the accomodation will need to be stronger. What about cats, racoons and rats? They will take chicks and are very good at breaking and entering, so any wood used should be thick or covered in wire mesh, and doors should have good catches. Your climate will make a difference too. Chickens don't mind a little rain, and will tolerate heat and cold well, but extreme conditions will need special consideration, for example shade over runs, or roofs which slope away from the run to prevent rainwater turning it into a swamp. You need access to all parts, so a door at the back to collect eggs is vital. I use a lot of bad language collecting eggs from coops my husband built that require reaching in from a lidded top with sides that allow for his long arms.
Will the coop need to be moved by one or two people? A heavier arrangement may do well to have wheels at one end, or at least handles. I can move my heavier small coops alone only by rolling them, obviously this is no use if they need to be moved with chickens still in them! It may be better to set coops up with two or three runs leading away from it, to be alternated, thereby not requiring any moving, but some like to use chicken "tractors" as a type of lawn mower or self-fertilizing tiller. (We use pigs.)
There is no need to go to a lot of expense making coops, and I have put several together from virtually nothing, they may not be beautiful, but they do their job. No-one needs to build log cabins or pagodas for their chickens....(photos coming), but it's a lot of fun:)
Great links:
Old Jim's Fowl Page
Chiken Tractors and Permaculture
Straw Bale Coop
Some tips on coop design, with photo of stepped roosting poles