Go Fish is one of the first card games we taught our kids. If your kids are still small, this is a great first card game to play together. The rules are fairly simple and it helps them learn the concepts of pairs and like groups.
Deal everyone seven cards. Each player takes a turn asking any other player for a card that matches any card in his/her hand. If you get the requested card, you get to keep asking, either for that card or any other that matches something in the hand. Once you do not get the requested card the person from whom you requested it says "go fish". The requester then draws one card from the stack of cards left in the middle. If he/she draws the requested card, the turn continues. If not, then the next player follows the same pattern.
Once you get all four of a like card (all four 5's, or all four Kings) you have completed a book. As there are no more cards in this book, you then lay all four down together. Once all cards have been played out, count up your books. The player with the most books wins.