For the router you'll need a a 3/8" straight bit, an edge guide, 1/4"- and 1/8"-radius roundover bits, and a flush-trim bit with at least a 1-1/2" cutting length. Bits of this size are available only for a 1/2" collet. Some routers are capable of using multiple collet sizes. I was fool enough to buy a router that only had a 1/4" collet. More on that, later.
The best thing about this wine rack is that it is very easy to build. All you need is the basic understanding of woodworking and a few tools to get started. You can modify your wine rack any way you want or build in a design or color different from this one. The basic steps to build a wooden wine rack are the same for all variants. I have included here the video tutorial that I followed in order to build myself a pallet wide rack.
After you have all the holes clean, set things up for your glue-up. You want everything on-hand before you start - drill, driver bit, glue, roller or whatever you're going to spread the glue with, and four clamps for the corners. You'll need a flat surface to do the glue-up on - I used my hollow core door on top my bench base - and another somewhat-flat surface to put the other panel on. My folding table was still holding my oak countertop, which makes a great flat surface, but I want to make sure I didn't drip glue on it so I covered it with some painters plastic that was left over from the last bedroom we painted.