Adding on is usually a pain in the butt, so make sure you wouldn't really be better off just building a whole nother separate (maybe larger) coop.
If you *must* do an addition, the simplest thing is to run a shed roof off one side of the existing coop, with its roof attaching to the wall of the existing roof just under the eaves. PUT GOOD FLASHING THERE (on the very short section of wall between the edge of the old roof and the top of the new one), or it will turn into a leak and rot farm, especially if the pitch is rather flat as tends to be the case with this sort of addition.
With some structures, esp. those with metal roofing, it is not too hard to add longitudinally to the shed along the main axis -- just pull off the siding and trim from the side you'll add to, then build more shed out as far as you want, TIED TOGETHER REAL STRONGLY to the sills supporting the old part's floor joists and the plates atop the walls. It is easier, safer and a bit stronger to leave the old stud wall in place as an internal divider (you can take the siding off it, of course) but if you want to you can remove it once all the rest of the structure is in place. Then use more of the exact same type of metal roofing to cover the new portion, and put siding on, and there you go. Only a minority of sheds are really well suited for this kind of addition however.
Good luck, have fun,
Pat