If you want the hostas to look their best after being divided, you can split them in the spring just as they are coming out of the ground and have good-looking hostas for the rest of the season.
If you divide in late summer (3rd or 4th week of August for us in Minnesota), the hosta has a chance to get established before winter and will look great in the spring.
We have even divided hostas in late October and they over-wintered well. Just make sure to cover them with about 6″ of leaves or straw, and keep them covered until danger of frost has passed in the spring. This will help prevent the hostas from emerging too early from a warmer than normal early spring and then suffer from snow or frost damage later.
For more information and a step-by-step guide to digging & dividing hostas, visit our Dividing Hostas post! It includes video tutorials and photos!