As flowers fade, you should deadhead. Once blooming is done, I cut the scapes (stalks the flowers bloom on) back to the ground so they don't go to seed. This encourages reblooming.
When and how often do you recommend dividing?
Sam: It really depends on the daylily―usually anywhere from two to five years. When flowers become smaller than normal, I know it's time to divide. You can do this in the spring or fall. If I divide in the spring, I replant what I can and pot some of the divisions to share.