Well, I use Swiss-made Riwax and Badertscher pads. I prefer the Riwax pads, because they are finer, more durable and finish fantastically. They are just normal 16.5 × 5 cm pads for rotary/DA use.
I wash them in my little mini-washing machine in a normal cycle. A little liquid detergent or APC (I am using Finish Kare 121 now) - depending on the dirt/residue, and go! I rinse them twice in cold water, then a few times by hand, just to be sure... Then I wring them out and letting them air dry. I store them in Ziploc bags. In two years I had to return only one waffle finishing pad because of delamination.
During polishing I wash my pads in the sink, using a regular soap bar and a 'gentle hand massage'. Then I rinse and wring them out (pretty aggressively - they hold up fine!), or spin them out and continue working.