I am trying to add material to my tire and after I complete the steps to get the material and make it textured, I am told to hit the material button to see the material and texture as one. However, my blender doesn't have the buttons under the preview window on the right hand side as the instructed video I am watching has.
Well I think I might see your problem. If you are trying to view your textures through the 3D Viewport without the need to render the scene:
There is a button that should have a white ball with up and down arrows on it aka "Viewport Shading" is its name and it sits to the right of "Object Mode" button in which that button also has up and down arrows on it. Here is a pic:
The picture you see above is the editor or "3D View Editor". Now in this picture you will see that white ball im talking about next to the "Object Mode" button. Now click that ball in your blender "3D View Editor" and set it from Solid to Texture or if that does not work set from Texture or Solid to Material. If all else fails then try and get a recent version of blender.
Let me know if this does not help you in any way! :D