If a rig's textures aren't displaying properly, there are a few things you can do to fix the issue.
The first thing to try is to press the 6 key in Maya to set your viewport to textured mode.
If you do this and the rig turns grey or white, or if the scene is rendered and the rig displays as black, the most likely cause is that the texture file either hasn't been downloaded or has become disconnected.You can find a couple of solutions below:
Using AMP (AN01-AN06 and Creature workshops)
If you're using AMP, the first step to solving the issue is to make sure you have the texture/textures downloaded. You can do this by right-clicking on the rig asset file and hitting "Get Dependencies".
Using the Hypershade
If you aren't using AMP, first double check the downloaded file for the texture file and make sure you have the textures unzipped in the same folder as the rig.
If you have the texture file but it is still not displaying properly in Maya, you will need to reconnect the texture in Maya. To do this, go to "Window > Rendering Editors > Hypershade", open the Textures tab in the Hypershade and find the texture node for the rig which should be called "file1" or something similar. Select the texture, open the Attribute Editor, then click on the file folder icon, browse for the texture file and hit Okay.
Finally hit the refresh button and the texture should be re-linked. The rig should have the proper texture again when you hit the 6 key in the viewport.