The point of the game is to be all out of paired cards, and not end up with the zebra. Here's how to make it into a kids' game.

[edit] Steps

Take thick paper, like card stock, and cut into card shapes (rectangles), so you have 51 cards.
Write "Animal Match Up" on one side of each card.
Draw (or print a picture, and paste) a pig on two cards, a cow on two cards, a kangaroo on two cards, etc. under the animal picture write what they are and their letter. (example: C is for Cow, K is for Kangaroo).
Do this until you only have one card left, and there are 25 pairs of other animals. Make the last card a zebra.
Shuffle all cards so they are totally random.
Deal out cards to the left, and keep going until all of the cards are dealt.
Look at your cards, and put down all pairs.
Show no one your cards, and make sure you don't make it obvious if you have the zebra.
Have the dealer pick a card from any player's hand. If it's a match to one of their cards, then they should put it on the table.
The person the dealer took a card from should then pick a card from someone else.
Continue until only one person has a card left; a zebra. Whoever has the zebra loses.

[edit] Tips

give every winner a prize, even whoever lost, just give them a smaller prize. It's a great game for little kids.
ideas for animals: cows, pigs, cats, dogs, mice, hippos, elephants, guinea pigs, gophers, horses, lion, cheetah, jaguar, bears, deer, fox, goats, monkeys, antelopes, sheep, mole, llamas, leopards, Tiger, and orangatangs. (that's 25).