Measure the distance between the top and bottom lips of the mug. Cut 1/4" wide strips of the scrapbook paper to length with scissors or a paper cutter.
Clean the mug with rubbing alcohol and dry. Add a bit of the Mod Podge Dishwasher Safe to the brush and paint a little down the length of the mug.
Take a strip and lay it on the mug in the medium painted area. Lay it as straight as you can and smooth it out so that there are no wrinkles or bubbles.
Repeat with another strip and so on until you have covered the space with the medium you brushed on. Brush on additional medium and keep smoothing on strips of the paper. Do this all the way around the mug. Set aside to dry.
If there are any funky extra edges on the top or bottom of any of the strips, cut them off with a sharp craft knife.
Seal the entire mug with another layer of Mod Podge, making sure to get into all the cracks and crevices. Let dry and repeat. Let cure for 28 days before washing.
Notes
Make sure to paint every inch of the paper so it is truly dishwasher safe.