This is what I did to make over the ultra-basic LÄTT kid-size table and chairs. I was really tired of cleaning the not-overly-slick surface of the pressboard panels and wanted to do something more interesting with them.
We had a section of very nice decorative vinyl shower curtain lying around (we'd used it for a messy mat for eating or playing on, but I plan to replace it with something more rug-like). After I took apart the table and chairs, I cut the vinyl in appropriately sized pieces with about an inch extra on every side. Then I wrapped it around the edges and taped it tightly over the panels with duct tape and pushed/slid them into their grooves (this took a bit of work and some gentle hammering). The duct tape really only needs to hold the covering in place long enough for assembly, as the essembled items will secure it in place. Finally, I reassembled the chairs and table.
I like this because it requires no paint, no new tools, and can be done with anything, really, as long as it's not too thick (wallpaper, fabric or even clear contact paper laid on pieces of kid art would work great). Also, you can change out the decorative coverings easily if you or the kids get bored with the look.