Here are lots of kids card games with their rules, number of players and the kind of cards you need:
Memory games
There are many memory card games: Flip one card over and try to match it to another.
Memory
Go fish
Collectible cards
There are collectible cards which you can swap and battle your friends.
Pokemon, duel master and Yu-ge-oh are collectibles and then you can fight your friends. These games are very popular. Your cards have attack and defense and a special. There are many packs of these and very enjoyable.
Pokemon
Yu-ge-oh
Duel master
Battle time
Basic Cards
There are also basic playing cards(A,2,3,4,5,6,7,8,9,10,J,Q,K. Joker)
With these playing cards there are so many ways to play card games for kids. You can play by yourself-Solitaire. There are lots of different ways to play solitaire. There are also card games where you play in a group - Rummy and Snap!