The easiest way is to determine the radius you want, say 19" as an example. That will be the curve created by a "circle" with a radius of 19 inches, which is actually quite flat for short spans but a nice moderate curve for something as wide as your desk. Once you know what radius you want, create a baton of that length or a string of that length and fix one end such that the free end can be used for marking the desk top.
As for reducing splintering, I'd say a fine tooth blade on whatever saw you use, or just do the whole thing with a router. It's going to vary somewhat depending upon the material, though.