The first step was to clean them and let them dry.
Next, I spray painted them white with a basic spray paint and primer. There is no need to be perfect, as the paint is simply a base to decoupage over. I already had Rustoleum paint and primer on hand from another craft. The vases took a several rounds of painting, as I had to turn them a few different angles to get the entire vase coated.
Then, I just went crazy decoupaging!
Separate the ply of the napkins you want to decoupage with down to one ply. My napkins had three layers, so I had to peel off the bottom two.