Assuming your model geometry is good (I can't really tell from the screenshot), it becomes mainly a lighting, material and environment problem.
If you are going for a photo-realistic look, use Cycles for rendering. It will handle lights and shadows in a more intuitive way.
Is it suppose to be a styrofoam cup? A porcelain cup? Glass? Set up the material for the cup accordingly. Styrofoam would be almost all diffuse, with a Sub-Surface Scatter component. Porcelain would be diffused white, with an added layer of highly glossy top coat. Glass would be, well, the Glass material node.
If the cup material is reflective at all, you will need to set up the environment so that there is something to reflect off. After all, a mirror ball in a perfectly grey world will only look grey. Multiple Plane Emitters is a good starting point, they can mimic lights shining through a windows.