how to apply more than one texture at once

Hello, I’m new to Blender and I’m trying to follow this tutorial on making an eyeball. http://en.wikibooks.org/wiki/Blender_3D:_Noob_to_Pro/Creating_Pixar-looking_eyes_in_Blender
However I ran into a problem: when I try to apply the iris texture, the texture gets applied to the eye white as well. How do I make it so that the different pieces of the eye have different textures?

use the vertex groups for assign different material to the same mesh. :wink: