First read this. It's kind of generic but I don't know enough about your specific situation to get too specific.
Pat’s Big Ol' Mud Page (fixing muddy runs):
https://www.backyardchickens.com/articles/how-to-fix-a-muddy-run-chicken-coop.47807/
There are two basic ideas. First is to keep the water out to start with. You have to know where the water is coming from before you can figure out how to keep it out. Maybe a better explanation or even photos could help us understand that. Is the water coming in at ground level, blowing in from the side, or is your roof slope putting it inside?
The other idea is to get the water out once it gets in. Gravity will cause water to drain out if the water has a place to go. Sandy soils often drain pretty well while clay soils don't. But there are all kinds of in-between soils as far as permeability goes. Some soils can be hard to deal with. Is yours in a low spot where water drains to instead of drains away from? Why doesn't the water drain away?
Pat's article has several suggestions, one might strike a chord with you. The way I handled this was to fill my coop with a few inches of dirt to raise the floor above the surrounding area plus I put in a swale/berm system on the uphill side to keep rainwater runoff away. I have a lot of ventilation so if it gets a bit damp it generally dries out fairly quickly but it doesn't typically get that wet to start with.
In the Deep Litter Method you are turning your coop floor into a compost pile. Just like a compost pile if it stays too wet too long the microbes breaking it down become the anaerobic ones. The water keeps oxygen away from the microbes. The compost becomes sticky and stinky. It can be unhealthy. If the compost stays damp enough for those microbes to live and reproduce but dry enough that oxygen can get to them you get a nice crumbly compost that smells like rich earth. Mine stays so dry that those microbes can't live so it's not a true DLM.
You mention that it is muddy but you don't say if it stinks to high heaven or not. If it stinks I think you need to get rid of the water or keep it out to start with. If it doesn't stink you might be able to use the DLM. There are different ways to do this. Everybody has their own favorite bedding: wood shavings, wood chips, straw, hay, dried leaves, grass clippings, maybe even Spanish moss if you are in that part of the world. Some people toss in kitchen wastes or excess stuff from a garden. There is no one way to do this and not a lot of restrictions on how you go about it. If it works, great. If it doesn't you may need to clean it out and start over.
Good luck!
