Are you asking how people do weathering with paint? I don't think I know what "cover paint" is.
If you're wondering how people do weathering with paint, I'll tell you how I got the dirt and dust at the bottom of this tank to look how it does:
Personally, I think that dirt looks good; it's a paintjob I'm proud of! There are other people who do far more intricate weathering using weathering powders and stuff, but the effect I got was very, very easy. All I did was drybrush it!
Citadel Dry paints are very good for drybrushing, but their color selection for Dry paints is slim. I just took regular Citadel paint onto my brush, wiped most of it off on a napkin, then went wild drybrushing the bottom half of my tank in a light brown, in this case Graveyard Earth/Steel Legion Drab. I then went over it again, not going quite as high, with Kommando Khaki/Karak Stone. I made a point to get into some of the recesses since drybrushing doesn't usually get in those, and dirt does.
For actual mud buildup, one way to do this is with a mixture of PVA glue and an appropriate material. Fine basing grit or sand is fairly popular, and can be applied with an old brush. Often people will go over the clumps of mud again with gloss varnish after painting the model to make them look wet. I did something similar with PVA glue and snow flock:
I don't know if that's exactly what you were looking for, but I hope I could help!