Here are the rules, as posted by the University of Virginia:
There are two sets of 100 cards. On one set the complete five-line poems are printed. On the other set only the last two lines (“shimo-no-ku”) of each poem appear. Usually there are two players or sides. Each player takes twenty-five of the shimo-no-ku cards and spreads them in front of him or her. A third person, acting as reader, reads from the cards with the whole poems on them. As the reader reads the first lines of a poem, each of the two players tries to find the card with the corresponding final two lines. The first player to find the right shimo-no-ku card removes it from the playing area. If the card is in the opponent’s area, the player gives one of the cards from his or her own area to the opponent. The first player to get rid of all the cards in his or her own area is the winner.
Very similar to another set in the Cotsen Children’s Library (CTSN): Cards 55195
See also Peter McMillan, One hundred poets, one poem each: a translation of the Ogura Hyakunin Isshu (New York: Columbia University Press, 2008). East Asian Library (Gest): Western PL758.5.O4 A3 2008