You can create a new material in two ways: modifying an existing material, or creating a new one from scratch.

Modifying an Existing Material

In this example, the cylinder has the material "Stones - Granite Sierra" and the plate below is "Metals - Antique Brass."

To create a new material from an existing material, find the existing material in the Material Editor, Then click New Material.
Assign a name for the new material. It will be placed in the same category as the original.
In the Pattern category, increase the Scale (which is the size of the repeated image, in drawing units), and change the various mineral colors.

This is the result - a larger scale granite with different colors.
For the plate, make a new material from the antique brass.
In the Reflectance category, increase the Mirror Factor.

This changes the plate surface to reflect the cylinder.

Wrapping an Image

If you have your own image you want to use as a material, this is defined in the Pattern category. This example uses a ceramic tile:

In the Material Editor, click New Category.
Assign the name "Tiles."
With "Tiles" as the category, click New Material.
Assign a material name. For the Pattern category, select "Wrapped Image" and click the Browse icon next to File name.
For Reflectance, use "Matte" with a high Ambience Factor.
Use "Auto Axis" for Wrapping.
This material is good for the cylinder, but the material used for the plate should be slightly different. Use New Material to create a copy of the tile material.
The Wrapping here should be "Z plane" so that only the top face of the plate will be covered.

Here is the result with "Auto Axis" applied to the cylinder and "Z-plane" applied to the plate.
If you want to change the aspect ratio of the tiles on the cylinder, switch to "UV" and increase the "U scale."

This makes the cylinder's tiles twice as wide, with the same height.