Hi Ann, and welcome to the Forum - and to chicken keeping.
The sort of run you make will depend a lot on how many birds you want to keep, and how much space you can give them. As a general rule, you will need to allow at least two sq. metres of run space per bird, as overcrowding can lead to stress and feather pecking. Also, very small runs are harder to keep clean. Many coops are sold with small runs attached, which have room for more chickens in the coop overnight than will be happy in the run during the day, also many of this kind of setup are hard to get into for cleaning and catching the birds when required. So its best, if you can, to instal a good strong predator- proof walk-in run, and put your separate coop in there. If you can roof the run, or even part of it, it will be much less likely to become a mud bath in winter and will be more comfortable for both you and your birds.
If you have an area of established grass large enough for the birds to range over, that's good, but if you are starting with a smaller run, grass isn't really very practical as they will soon scratch it all up and eat it and then you will be back to mud bath again. There are various ways of keeping it dry underfoot. Some people use slabs, and if so, its good to put a deep litter bed on top, either wood chippings or Aubiose (shredded hemp stems) or similar, as this is softer and warmer and the hens can dig around in it. When we were making my run, we put the same galvanised mesh as we used for the walls and roof all over the floor as well, to prevent rats etc. digging their way in, and then I topped it with permeable landscape membrane, well pegged down at the sides, with Aubiose on top. This drains well if the run isn't roofed and lasts a long time. It's easy to pick up the poos daily and just top up when necessary.
There are quite a few threads on here in the General Chickens section, about making runs, which you might find helpful. If you could give some more details of your plans so far, people will be happy to help you with ideas.
Meanwhile I will move your thread to the Genaral Chickens section, rather than Chickens Health, as I think you will get more replies in there.