You can create 3D curves based on the surface of a model, or create 2D curves on the screen plane. Mudbox recognizes whether you are drawing on a model or in empty screen space, and creates either a 3D or a 2D curve accordingly. See also Curves.
For complete task information, see:
To extend a curve, connect curves together, close a curve in a loop, change the shape of a curve, or smooth bumps in the curve, see Modify curves.
Once you have curves drawn in the scene, you can use them as a guide for your sculpting or painting. See Sculpt or paint using curves.