Trim. Dig. Dump the clump into a tub of water. Swish and let the roots soak for a bit. Take it out, and blast it with the hose to rinse the rest of the dirt off (transferring the dirt to yourself and everything else within 10 feet of you in the process). Use two large screwdrivers, carefully placed, and wrestle with (er, divide) the clump. Swear with each fan that you snap off at the crown. Once everything is divided down, rinse it off again and leave it all somewhere to dry, while you stagger inside to wipe the sweat and dirt off, get a cold drink, and just generally collapse.
I'm digging and dividing irises right now. It's not as dirty and messy and just plain hard as digging and dividing daylilies, but I can't say that I'm enjoying that either. As for the daylilies... I have some YUGE clumps which need dividing... but that is a chore that I prefer not to think about doing.
Certainly not in this weather, anyway.
(I thought that spring or fall were the times to dig and divide? I recently, stoopidly tried potting up a seedling I wanted to save, and promptly killed it via rot. I should have just left it alone until October.)