Hope this is OK but for some of the best info on leatherworking I HIGHLY recommend
1) Burnishing smooths and polishes the leather - it can be done on both the edges as well as the face, the latter is something not commonly done today but was common on period leather
2) Rounding the edges is best done with an edging tool, there are several types and sizes dependent on usage and thickness of the leather. These are used first before burnishing - they "trim" the sharp corners off. JWP makes several types - here's the most common - these are high quality tools and worth the price but Tandy, CS Osborne, and others sell less expensive models
3) Edge burnishing can be done by hand or machine. There are several types of mechanized tools that can be used for edge burnishing - some are just chucked into a drill while others are dedicated tools with their own power source. Various types of such machinery were at times used "in period" - the use of machines is not a modern thing at all.
4) Using Gum Tragacanth, a natural vegetable glue, is a big aid for edge burnishing as it "glues" the fibers together.
Along with using punches of various sizes I use a clicker knife for tight curves - you can see one here - they take various types of blades:
For the tighter curves I use the curved blade and hold the leather in hand (if of adequate stiffness) and cut sort of like peeling an apple - if that makes sense???
You can then cleanup the edges of any knife marks if need be by using a Dremel or drill with a sanding drum or by wrapping a dowel or metal rod of the right diameter with sandpaper 100-150 grit works good -