I wouldnt say I do anything as a consecration as such, I just shuffle, more to get a feel for the deck.
I also always do a new deck spread with any new deck.
I usually consecrate the cards with the four elements. Now I don't recommend setting your cards on fire or putting them in water but you could invoke the four elements and ask for their blessing on the cards. Then possible dedicate the deck to your favorite deity associated with oracular gifts.
some people just pass their deck through the smoke of a consecratory incense (frankincense is high on the list that people use but some prefer a blend of sage and sweetgrass) and dedicate the deck to their purpose.
in Scott Cunningham's book Incenses Oils and Brews he gives this recipe for divination incense:
2 parts sandalwood
1 part orange peel
1 part mace
1 part cinnamon
To me this is an ask on how to cleanse cards of prior influence.
Typically I bury my cards in kosher salt... but... if the cards "feel good" on first handling, I'll not do so. I've found that the cards mostly want to be heard and often have energy busting for release - mainly because they've been boxed for a while. You can put your new deck in a wooden bowl and let them "rest" a bit... 3 days is a good measure... and then pick them up. But really... shuffle them a few times to get a good feel. A deck has a personality... listen to that... it'll let you know if it likes you or not.
I like to sit with a new deck and just shuffle them for a while and connect with themand charge them with my own energy, some people say blessings when they first shuffle, some smudge it just depends on what you want to do, then ofcourse you could do nothing!