Lots of other threads discuss this in more depth, but a Readers Digest version (as per me, anyhow
) is, like:
1) first make sure you have done everything possible to limit water inputs. Install gutters (yes, even on a chicken coop!) with downspouts that take the water
well away from coop and run. Trench around the run, with an additional trench leading away to lower ground. If you can roof all or part of your run, that helps too.
2) I'd really advise against adding sand or gravel while the ground is muddy. They will disappear fairly quickly, leaving no sign they were ever there. Wait til the ground is REALLY DRY (like, next summer) before adding them. Then, add a sufficient depth (like 4-6") and they will serve you well.
3) Best temporary mud fix is to add a COARSE, relatively rot-resistant organic material, like hogfuel, coarse bark chips, coarse woodchips, etc. You can use finer tree chippings or straw or hay but they will disappear much much faster. ALL of this will gradually rot down and disappear, adding substantially to the wetness and intractability of the mud, so organic stuff is just a temporary fix. In spring, rake it all out (good in compost pile or garden) and replace with sand, gravel, or sand/gravel mix. Of course you can top up the coarse organic material as needed while mud season is still in effect.
DO NOT get talked into landscape fabric or geotextile, unless you somehow have the luxury of burying it a foot or so deep where the chickens cannot dig down to it, rip it and eat it. DO NOT put shavings in the run, they'll turn to worse mud Real Fast. Also be very very cautious about suggestions that you, basically, aerate and loosen your soil... unless there is somewhere good for the water to drain TO (i.e. you are just breaking up a hardpan layer), you will just create more lasting mud ('the clay bathtub effect').
Good luck,
Pat
