I normally don't clean my pads. I usually toss them or sell them once I'm done with them, but I understand that it's a little impractical to do that. The Griot's Garage Microfiber & Foam Pad Cleaner is what you need if you want to reuse your pads after polishing. This will remove all of the residual polish and polishing oils from your pads.
What you do is take your pads to the sink and spray the cleaner on the pads and agitate them with the Rupes claw tool. Make sure you rinse thoroughly and allow the pads to dry before using again.
You can use this as a compliment with normal fabric detergent to wash microfiber towels, but P&S Rags to Riches is what I recommend you use for towels. I exclusively use this on my pads.