I've discovered a good way of cleaning Tarot cards. I bought a second-hand large Thoth deck and some child had been at it; I had to cut off two small chewed corners. To clean them I used the often-advertised magic sponge.
You can see then at
http://www.amazon.co.uk/gp/aw/d/B003QITQC6 but I actually buy mine at Pound land.
Use just a small amount of cold water and wipe the cards, one at a time, gently. If you rub then the print will come off the cards. Dry then immediately with a dry tea towel - ie not one that has recently been used. Don't forget to write around the edges of the card.
Mine came out really well!
NB practice on a similar-feeling playing card first!
Sincere & fraternal regards
Alan