Mudbox can't rig models. It's only for sculpting and texturing.
The general process is that you build your low-poly model in something like 3ds Max, Maya, or (for a free program option) Blender, then you would export to Mudbox (as an .obj file) and you would sculpt the detail into the model, and perhaps texture it (otherwise you would create the textures in Photoshop). Then you would use Mudbox to render out a normal map for your mesh and you would apply that to your low-poly model so it would have the extra sculpted detail. Then you would rig your model in 3ds Max, or Maya, or Blender and export to UDK.
Rather than starting from scratch, you could export the lowest or second lowest subdivision level of your model from mudbox, then bake out a normal map of the highest subdivision level to use on your character.
The one problem you'll probably run into is that the topology for your character would probably be no where near ready for rigging/animating since you most likely didn't start off with a properly topologized base mesh. You'd have to fix the topology in a different 3D app so it will animate properly.
From there, you'd have to use maya, max, or some other program to rig it and paint the weights properly since mudbox can't do that. You have to make sure the bone names match the bone names of the UDK rigs, then when it's imported into UDK you can assign the different animsets to it.