Kale,
I can make those pieces with a router and a table saw pretty easily.
If you look at the picture you posted, you will see that the piece on the right is a template. You can make that template out of 1/4 fiber board, MDF, etc... Use a table saw to cut/make the outside dimensions, then use the router and a circle template to make the outer and inner curves.
This is my router and circle guide:
If you only need a 90 degree curve (like in the corners) then you only need to figure out what dimensions you want for your radius. Come in that far from the sides and your center point is where the lines cross. Drill a hole there and use your circle template to cut the curve. The same holds true for a 180 degree cut. Just figure out where you want to radius out from, and go from there.
Once the template is done, you can use that to rip out your pieces. There is a router bit available that has a ball bearing guide at the bottom that allows you to use the template under the MDF piece you are cutting. Just rip the MDF to the proper outer dimensions and follow up with the router.
Once that's done, come back with a round-over bit to make the smooth edge. (It also has a ball bearing guide to keep it straight.)
Here is an example of a grill I was making for a set of tower speakers we were building. You can see it's still in rough form:
We followed up with a round-over bit on the outer edges and covered it with grill cloth.
Would it help to make up some videos on how to do this? I could probably take some video during my next project and put it on my server for you guys to look at.
Mark