You can control the colors a single material has, per face, in various procedural ways, or you can UV map your object, and its material can refer to a texture map, assigning colors in any way you like, across the surfaces of your object.
But here, you probably want to assign separate materials to each face.
- Click the '+' sign next to the materials list currently showing 'Material', highlighted. This will create a new slot.
- Press 'New' below the list, to create a new material, or select a material you have already created, from the dropdown accessible just to the left of that button.
- If the material is 'New', give it the color/ other characteristics you want.
- With the desired material active in the list, and the desired faces selected in Edit Mode, hit 'Assign'. The selected faces will acquire the selected material.