Along with traditional art principles it is key to have a comprehensive knowledge of certain software. In total I have a sound understanding of three applications however having a basic knowledge of more than this is not only required at times but will make you more employable plus more of an asset when employed.
Many people know that Photoshop is a key tool. It's what you will be using everyday so nothing less than a comprehensive understanding is what's required. It's a DMP's bread and butter.
Being more than familiar with Maya is very important. Maya is an absolute goliath of a package. I've been using it heavily since 2011 and still feel like a novice at times. In my opinion being able to do the following is essential before your first job in DMP.
From my first paid job to present I frequent these tasks on a regular basis.
Modelling - by no means do you have to be able to model something as complex as an anatomically correct human being or be as accomplished as somebody doing this profession but you must have a basic knowledge. Being able to model hard surface objects along with basic geometry for projection is the bare minimum. In addition knowing how to sculpt is extremely useful, if not in Z-Brush then in Maya with the scuplt geometry tool.
UV texturing - being able to texture objects from creating UV's to assigning textures is very important. Of course if you're an environment artist or more of a CG guy this is given but as a DMP being able to get yourself out of a problem with CG is very useful at times. UV texturing is a key part of that.
Camera projection and an understanding of how to bake camera projections into an objects UV's - camera projection at present and for the past 10 years or so has been done in Nuke. That being said understanding camera projection in Maya is very useful. With recent DMP scripts and the addition of Viewport 2.0 projecting in real-time is now a possibility in Maya. This means modelling to projections which is a very useful thing to be able to do. In my experience this makes the process of creating camera projection much more intuitive, saves time and increases accuracy.
Being able to bake projections out as textures is another practice which is very useful. This of course can be done in Mari but from my experience doing so in Maya can be enough, depending on your brief.
Lighting - knowing as many renderers as possible will really help but a good knowledge of Mental Ray, Arnold and V-Ray is what I've found to be enough. Chances are most studios at present will use one of these renderers in their ENV department.
As I previously mentioned sometimes in DMP getting yourself out of trouble with CG is very important. What I mean by this is that primarily DMPers work with photography. If you can't find the right image you need then being able to render an element in CG instead can save you. Being able to light that element properly is cruical. This again relates to an understanding of how light works, as I previously mentioned too.
For nearly ten years now, Nuke has been a large part of the DMP toolset and a comprehensive knowledge of this program is essential. Being familiar with a camera projection workflow along with a multiple projection workflow is absolutely key. Understanding the basics of compositing in Nuke will also go a long way when working as a DMP. Colour space, roto, keying and working with lens distort nodes, to name a few, are some good things to know.
For Maya and Nuke there are countless tutorials available. For learning Maya Digital Tutors is a great resource and for Nuke as well. Additionally for Nuke the DMP section of the Gnomon Workshop is a good place to start. Watching as many tutorials as possible from the Gnomon Workshop will really go a long way in learning how to do DMP initially but what is one of the best ways to learn is by getting production experience when you're ready.
As I've just mentioned Photoshop, Maya and Nuke are key tools to know for any DMP but there are many secondary tools available. Knowing as many pieces of software is very useful but the ones I found myself using on a regular basis in the industry which aren't the three I've just mentioned are Photoscan, Speedtree and Mari to an extent.
Something which should be mentioned here is that I've listed Maya as my primary 3D application. That is not to say that knowing 3DS Max or Cinema 4D to name a couple of other 3D applications instead of Maya won't land you a job in DMP but from my experience knowing Maya first and foremost makes you more relatable to employers. All of my past employers have used this piece of software as their primary 3D application.