Ok, I made the vases to see how it went and I have a few pointers (and pictures!)
There's 2 different vases - 1) With wood grain contact paper and 2) With wood veneer "spots". Let's look at #1 first.
Wood grain contact paper vase
The original pictures use a straight cylinder and I would recommend that for this project. It makes it easier to cut the contact paper into strips and wrap around with out creasing. I haven't tried another shape, though, and it might be workable.
I cut several different shades of metallic and wood grain contact paper and wrapped them around the vase
Lather, Rinse and Repeat . . .
I added some decorators rocks and floating candle and voila . . .
Veneer Spots vase
The original instructions call for peel'n'stick veneer sheets. I couldn't find peel'n'stick, so I used the glue on type. It worked pretty well, a couple of thoughts:
1) Veneer is quite expensive ($17 for a 12x48 sheet). The original vase was covered in spots (and looked cool), but I decided to cover only part of the vase to conserve veneer. I like the way it turned out and I think different patterns could use only a small amount and have a striking effect.
2) Since I couldn't find peel'n'stick, if you want to make this vase, I would suggest using a vase that has a flat surface. I haven't tried it on a curved (might work), but flatter would probably be easier than gluing