1) there IS NO "the" deep litter method. There is a whole spectrum of different ways of managing floor litter that involve depth of bedding and, in some cases, a degree of in-situ composting. It is a giant mistake to think you can follow a recipe and have magic occur... what works well for one situation may work poorly in another or backfire badly in yet another situation. You need to find what works best FOR YOU, through experimentation, preferably without being overly wedded to one partiuclar expectation in advance.
2) Supposing you're talking about versions where you have your bedding dampish and expect composting to occur in it, you do not NEED a dirt floor but it sure helps a lot. It is generally a mistake to try it on wood -- you end up rotting the wood -- but can be done to some degree on a slab floor or pavers or stall mats. It will go a lot faster if you chuck several shovelsful of good garden dirt into there once the poo has built up a bit, and stir it in well to the bedding. And you often need to work harder at keeping the thing sufficiently damp.
But, again, damp composting type deep litter is NOT a good idea for everyone -- indeed I would say that it will only work well for a minority of peoples' situations -- so you may not even WANT it to occur in your coop, once you discover the realities of the situation.
The two main advantages of a dirt floor are a) cheap and b) good thermal mass.
The two main disadvantages of a dirt floor are a) very vulnerable to rats and digging predators, and b) prone to flooding/muddiness.
If you choose to do a dirt floor, you definitely want to have plans in place to deal with those two issues.
Good luck, have fun,
Pat
