Now that you've been introduced to materials, how do you use more than one material on one object? Open the materials panel and look at the box with "Material" highlighted in blue (Figure 1). These are the material slots, and this is the section you will use to assign multiple materials.
First, delete the cube and create a UV Sphere. Then, instead of adding a new material, just select the material icon next to the material name to bring up the material list. Choose "Material" and rename it to "gray". Note that when there is only one material in the slots, that this is the base material of your object. If there are multiple materials in the slots, the material in the top location is the base material.
Figure 1: Material Slots
Next, hit the "+" next to the material name to add a new material based on the gray material. Change the name from "gray.001" to "red" and make the diffuse color swatch a red color (Figure 2).
Figure 2: Add "red" material
Now we have two materials: "red" and "gray" in the material list, but only the red one now appears in the material slots.
Add a material slot
We now need to add another material slot. Locate the "+" to the right of the material slot box. Use this "+" to add another slot by duplicating the currently selected material slot. Note that this is different from duplicating a material. Another "red" material slot is created (Figure 3).
Notice that when you duplicated the material slot, that a "2" appears to the right of the material name field. This number indicates how many "things" have this "red" material linked to it... or how many "users" it has.
Figure 3: Duplicate "red" material slot
Change a material slot
Now we want to make one of the "red" material slots into our other "gray" material. It's really simple: just select the slot you want to change and select the material you want from the material list (Figure 4).
Figure 4: Change one "red" material slot to "gray" material slot
Now all we need are some faces to assign the slots to. Go into a front view, in wireframe, change to Edit Mode, change to face select mode and select only the bottom half of the sphere with the Border select tool (Figure 5).
You might want to save your selection in a vertex group. If you worked with any prior versions of Blender, you'll remember the vertex groups were right next to area where you created multiple materials. Now, they are located in the Object Data section of the Properties panel. Just hit "+" to add, rename if you wish, select faces and Assign.
Figure 5: Select bottom faces of sphere
Assign a material slot
While still in Edit Mode, look directly beneath the material slot box and notice there are now three buttons: Assign, Select and Deselect (Figure 6). These buttons only appear while you're in Edit Mode, which makes sense considering you are assigning materials to different components of your model. With those faces still selected, hit "Assign" and watch the bottom faces turn gray (Figure 7).
Figure 6: Assign/Select/Deselect options appear in Edit Mode
Figure 7: Assign "gray" material slot to selected faces
Tab back into Object Mode and look at your model (Figure 8). You could have assigned the faces on the top half as well, but there's no need to. Whatever you don't assign to a material slot will assume the base material, which is the material slot at the top of the list. In this case, that is the "red" material.
Figure 8: Result viewed in Object Mode
Remove a material slot
Now that you know how to add a slot, let's look at how to remove one. First, though, make sure you're in Object Mode or you might get strange results (if you see a material turn black while removing a slot, tab into Object Mode and Undo a couple times).
Select the "red" material slot and hit the "-" to the right of the material slots. The red material slot disappears and your model turns all gray, because now there is only a base "gray" material on it.
Next, add a new material by duplicating the gray material with the "+" by the material name field. Change "gray.001" to "green" and make the diffuse color a green color. Add a material slot by duplicating the "green" material slot. Then, select the top material slot and change it back to gray from the material list so that gray is the base color (Figure 9).
An alternate, quicker way of doing this would have been to use the "+" sign on the material slots to duplicate the gray material slot. Then with the second "gray" slot selected, you could add a new material, rename it and change the color.
Figure 9: Remove "red" slot and add "green" slot
Tab back into Edit Mode and select some faces. Again, use the Assign button with the "green" material slot selected to make those selected faces green.
Figure 10: Assign "green" material slot to selected faces
One final button to take note of is the "down arrow" to the right of the material slot box. You don't really need this button for multiple materials. But, since it's in the vicinity, click on it to reveal three options.
Copy Material to Others will copy the active object's material datablock to any other selected objects.
Copy Material will copy the properties of the selected material (not the datablock or material name) to the clipboard.
Paste Material will paste the properties (not the datablock or material name), previously copied onto the clipboard, onto the active object.