Many people seek information about cleansing their Tarot decks for various reasons. I don't feel the need to cleanse my own, but that doesn't mean the practice isn't right for anyone. For those who do believe it works, or at least that it COULD work, there are several ways suggested for doing it.
Some advocate using salt to cleanse a deck. Putting a ring of salt around the deck and leaving it for 24 hours would be a suggestion, leaving it undisturbed in a safe place so the salt won't be disturbed and contact the deck. One could put the on a bed of salt, but if doing that, I think I'd wrap the deck in a thick-ish cloth to keep the deck away from actual physical contact with the salt. White sage is effective, some say, and if it were me, I think I'd crush up some dried white sage leaves and combine them with sea salt or that pink Himalayan salt.
White sage smoke is sometimes recommended. Passing the entire deck through the smoke, or passing each individual card through sage smoke may be a method that appeals to some. If choosing this method, I suggest you use one of the little charcoal briquets used with incense because white sage smudge sticks are hard to keep smoldering. They tend to smolder out quite quickly. Using a briquet and crumbled sage and stem bits would work better. Keep your supply of crushed leaves and bits nearby so you can sprinkle more on the lit briquet if your smoke stops. A smudge stick may produce smoke long enough to run the whole deck through once or twice, but if you're doing the whole deck doing each individual card, the lit briquet with the supply of crushed leaves and bits in a small dish nearby will make the task much more enjoyable and efficient.
I have an essential oil blend called Healing Oil and another called Altar Oil. I suggest putting a light coating of a similar oil on one's fingers and/or hands before shuffling the cards well several times. If you have no suitable oils with healing properties, then choosing some dried herbs with healing spiritual properties would be helpful. Put the deck in a box or bag with a little sachet of the healing herbs in with it for a few days. However, even dried herbs contain oils that might stain your cards, so take care not to place them in a very sheer bag that will contact your deck.
Stones can be a preferred choice for some people. However, I wouldn't suggest using crystals because they generate energy and you wouldn't want to perpetuate or boost any bad energy you're trying to eliminate. I'd suggest small tumbled stones of other types with known cleansing energies rather than crystals. With respect to crystals, one type I'd especially avoid is smokey quartz crystals in this case, because of their darkness. They have positive effects, but in the case of dark energies, using a dark crystal would be counter-productive, in my opinion.