Models should be exported from MasterpieceVR as an FBX.

The first thing you should do is make sure your model has vertex colors. You can see your vertex colors under the "Properties->Object data->Vertex Colors".

For my workflow, I work with the cycles renderer.
Setting up the material to use vertex colors is pretty simple. Add an "Attribute" node. We need to enter the name of the vertex color data into this node. For me, it's "Col". Then you can connect it to the color input of the "Diffuse BSDF" shader, or whatever shader you need.

Now, after you've set up some lighting, your model should have its color when you render!