Before getting it wet, I usually just bang it against the inside of a trashcan just to remove a lot of the debris. I then do the rest of the cleaning under a running faucet. I don't use any soap, but I suppose doing so wouldn't hurt. You need to open up each fold to get the residual dirt out. Also need to get at each end of the fold as the dirt runs to the ends. An old toothbrush helps. Whole process takes less than five minutes. I don't think swishing it in a bucket of water will do a good enough job.

Having said all that, I must admit that I've never read the brochure to see what it says regarding cleaning methods.

Hope this helps.

Part 2...

Never had anything close to resembling mud. Perhaps the "dry-banging" against the inside of the trash can removes most of the dirt that's collected. Most of what's left is just residual dust and fibers. Sounds like you've already done a good job at getting as much dirt out as possible, so your wet-cleaning should go quite well.