When the days are cool and if the ground is moist, most perennials are very forgiving about being divided, even quite late in the fall. They just need a little time for their roots to re-establish themselves before winter comes.
It is best to dig up the whole plant and then slice the roots into chunks with a sharp knife. Remove any weeds that may be lurking amid the stems and roots and reset the divisions, pressing the earth firmly around the roots before watering well. This is what English gardeners call "mudding the plant in."
If there's a lot of tall foliage, it's okay to cut some off as long as you leave some top growth with leaves. Sometimes if the clump is too big and you can't get it all out, you can cheat and just slice off an outside chunk with a sharp spade. I often do this when I have, for example, a large stand of Siberian iris.
Remember, however, that plants with long tap roots, such as butterfly weed and oriental poppy, don't divide well. Sub shrubs such as sage, lavender and candy tuft and perennials with single stems can't be divided.
Most gardening books provide a list of those plants which resent being interfered with, so if you have a favorite plant, check a reference book before you start to dig. Otherwise, grab a spade and remind yourself that most gardeners learn their best lesson through trial and error.