How do you read a deck of cards?

[sordini]

Clubs, hearts, spades, diamonds.
Ace to ten, Jack, Queen, King

Is there a special way of saying these things?

[Toritoribe]

Clubs, Queen are sometimes called 三つ葉[mitsuba](= three leaves), 女王[jouou](= queen) respectively. But, interestingly, King isn't generally called 王[ou](= "king" in Japanese).

Ace, Jack, Queen, King are sometimes also called 1[ichi](= one), 11[juuichi](= eleven), 12[juuni](= twelve), 13[juusan](= thirteen).

[sordini]

Toritoribe: Thank you very much for the guidance information. I hope these are OK:
初さんhatsu san (3 of hearts)
好き五suki go (4 of spades)
三つ葉七mitsuba nana (6 of clubs)
混合女王kongou jouou (Queen of diamonds)

[Toritoribe]

Uh, those don't make sense, I'm afraid.

ハートの3[haato no san] (3 of hearts)
スペードの4[supeedo no yon] (4 of spades)
クラブ/三つ葉の6[kurabu/mitsuba no roku] (6 of clubs)
ダイヤのクイーン/女王/12[daiya no kuiin/jouou/juuni] (Queen of diamonds)
(Probably what you wanted to say would be 金剛(金剛石=diamond), but diamonds of cards don't be called 金剛.)