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I use an all purpose cleaner like Meguiar's D101 or D108. I also have a floor mat cleaner made by Chemical Guys that does a nice job as well, but probably isn't worth the extra price.
What you don't want to do is put a typical protectant (like Armor All, etc.) on the mat since this may increase the slickness of the mat and as a result your ability to slip around.
+1. That's what I do also. The weather tech mats actually fit in the Tesla better than any other weather tech mats I have bought for previous cars. Originally I was hesitant on buying them for that reason. But the service center had them there and put them in for me to see.
When mine get really dirty, I take them out and put them on my driveway, spray them with Simple Green and scrub with a bristle brush, then hose off and let dry. But I only do that a few times a year.