Here is a list of the paints and tools I use for these specific bases.
1. Dirt from the yard or a flower pot. I prefer it from the yard because it doesn't have perlite or vermiculite in it, but since my yard is made of sand(?) I have to use flower pot dirt.
3. A flat "drybrushing" paintbrush.
4. A base (duh)
0. Surface Primer (Vallejo)
1. Oak Brown (Army Painter)
2. USAF Green (Vallejo Model Air)
3. Desert Khaki (Reaper Master Series)
4. White (Vallejo Model Color)
5. Brown pigment; I don't remember the name. (Vallejo Pigments)
6. Faded Green pigment (Secret Weapon Pigments)
I start by gluing the dirt to the base. I let the dirt dry out for a couple days first. Its something I recommend doing during a period where you don't feel like painting that way you aren't waiting on it do dry before doing a project. I've heard you can bake it in the oven if you want it to dry faster, but I've never tried it, plus it might destroy any tiny roots you might have in the dirt, which are really awesome looking on the base as small branches and roots.
Next I water down the Oak Brown to the consistency of water. When you apply the mixture it should soak right into the base. I usually do the more rocky looking parts in brown and the finer textures in green to simulate moss and such. The dirt should vary in size so you get a more natural look. After this step you should have a very pale base.
I use a hairdryer on the low setting to dry the base. It should be pretty watery so if you add any more paint at this point it will just blend in and not really add anymore color. After it is dry I paint it with the same colors, but at "normal" consistency for painting a miniature. Don't go overboard on trying to get the paint in all the crevices. After you are done painting this step you should notice that the deepest parts are still the lightest. That is the way it should be.