I have done a few projects now with beadboard wallpaper. It is pretty inexpensive ($15-20 a roll), fairly easy to use, and can create some great spaces/things. I covered some diaper boxes for Johana's room for organization and was going to do the exact same thing for my nursery. Then I saw a partial roll of beadboard wallpaper that I had leftover from covering the ceiling in the playroom, and I wondered if it would work to cover cardboard boxes. So I took some diaper and wipe boxes, cut off the flaps, and set to work.
I used my rotary mat and ruler to cut a separate piece for each side. I followed the directions on the wallpaper for and made sure to try and let as much water drip off of it as I could before I put it on the box. I had better luck just doing one side at a time. I would put the wallpaper on and make sure that it laid flat until it had dried. I also had better luck if I left a slight overhang on the long sides. Once they dried, I folded them over and hot glued them down to keep it tight. I also ran some hot glue around some of the edges that didn't seem to stick as well, pulling the paper tight as I did so. Then on the short sides, I cut the wallpaper just a little bit shorter than the side and overlapped the flap that I had already glued down.
Here you can see there are a couple of wrinkles because all of the edges didn't stick. This is what I tried to fix by hot gluing the edges down.
To create a basket liner look, I took some cute scrapbook paper and cut it into 4" strips, and then Modge Podged it across the top. I also left a litte overhang to fold over the top of the box. Again here, I had better luck just doing one side at a time, letting that dry, and then moving on to the next side.
Because the paper I used was only 12" long, I overlapped multiple pieces to get it to go around the entire box. Most of the wrinkles fell out of the paper as the Modge Podge dried, and although they are far from perfect, it was an inexpensive way to get some cute storage containers.
Because these boxes are going on closet shelves, you won't really be able to see inside of them, so I didn't worry about covering the inside at all. I think for the next few that I cover, I will make the overlap on the top a little bit bigger so that the scrapbook paper covers a little bit more of the inside.