Welcome to BYC. Where, in general, are you?
Climate matters and some thing are only locally available -- such as the pine straw that I love in my run (only available in the US southeast).
The coarse wood chips
@aart recommended are often considered the gold standard for mud control but you might also need to address drainage problems.
It looks like there is a slope right next to your coop/run and at least one other structure nearby?
If the water runs off other buildings or down a slope into/through your coop/run you'll need to put up gutters to direct water away, dig diversion ditches, and/or put in French drain or grass swales -- whatever is necessary to get water to flow around the coop/run instead of into/through it.
If the coop/run is located in a low area where water collects your best option is to move the chickens to higher ground. Alternately, you can add fill to build up the level of the ground so that it's no longer a low spot, but this is best done by a professional (who is worth his weight in gold for solving serious drainage issues with intelligent re-grading).
If it's just heavy rain causing an intermittent problem then you need to add plenty of dry organic material such as those wood chips and might consider roofing all or part of your run.