By hand? It'd be pretty tough. Do you have a router or jigsaw, preferably table mounted? The arcing slots would be tough to pull off that way, but they could be done straight pretty easily.
Both the base and the lid for it (not in that diagram) have matching slots for a mesh cylinder that sits just inside of it. That way cleaning the mesh is is easy as pulling the cap off and sliding the mesh out to give it a quick rinse.
After getting a couple of these built, I think I'm also going to try an alternative version that's almost completely open that basically just serves as something to hold the mesh in place. We'll see what ends up being functionally and aesthetically better.