Well, not a computer, except for scanning and e-mailing. 
I paint everything traditionally with animation cell vinal, available from www.cartooncolour.com.  The paint is incredibly versatile, allowing for washes as well as opacity, depending on the amount of water you mix in.  I get textures right on the board using paper towels, sea sponges, dry brush, toothbrushes, and my fingers.  Brushes vary, but usually I'm using a watercolor brush for linework and a big flat watercolor or acrylic brush for bigger shapes.  I paint on 2 or 4 ply cold press illustration board or 300lb (or more) cold press watercolor paper. 

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