Herbaceous are essentially plants which mostly die back every year to ground level so you would cut away any dead foliage at the end of Autumn simply to keep the plant looking tidy.   The exception to this rule might be if the seedheads are a food source to birds in your garden.  A few herbaceous are actually evergreen or semi-evergreen - some hellebores fall into this category and you would leave the foliage intact to protect young Spring growth, and then tidy up any sad looking bedraggled leaves in late Spring.
Propagation can be achieved in several ways -sow seeds, although quite often seed doesn't come true, root cuttings and finally division which is the most popular method although not suited to all herbaceous.   This last method involves splitting the plant up using a sharp knife or inserting two garden forks back to back to each other into the dormant plant and easing them apart by pulling the handles together.  Each of the young plants should have some nice healthy roots and buds which will form leaves in Spring.