Grab your old magazines and books (I got mine for 99 cents each at a thrift store) and cut out a whole bunch of circles! Try to stick with some sort of color scheme.
Take off the lamp shade and get your hot glue gun hot. Start gluing the first layer of circles to the bottom of the lamp shade. You will want to have a bit of overlap so that you can fold the bottom under as you go. Also, try not to allow any of the original shade to show through underneath. Do your best to make sure your circles overlap enough to avoid this. Once you've done your first row, you can continue to add rows starting wherever you'd like!
Continue this until you reach the top. You may want to periodically check to see if you have things spaced out correctly so that you're left with a good amount of space at the top for your final row. (This is where the pencil comes in handy.) When you're done, fold over and glue the top just as you did at the bottom. Gently pull off any hot glue "strings" and you're ready to put it back on your lamp!