The classic cardgame Go Fish.
Ask your opponent for the cards you want, and hope that he doesn't tell you to go fish!
Go Fish is a simple game that is popular with children (my 6 year old son for example). There are many variations of it, the rules here describe how it works in this game. It may not be exactly the way you are used to playing.
To collect as many "books" as possible. A book is four cards of the same rank. The player with the most books at the end of the game wins.
Dealing and setup
The game can be played by 2 - 4 players. First cards are dealt to the players, if there are 2 players then each gets 7 cards, if there are 3 players then each gets 6 cards and if there are 4 players then each gets 5 cards. Once the dealing is done the rest of the deck is put in a random pile on the table.
Asking and fishing
The initial player is selected at random. The player can then ask one of the other players for a particular rank. For example, you might ask Bill if he has any sixes. You may only ask for ranks that you already have at least one card of. E.g. if you don't have any sixes yourself you can't ask for them. If Bill has any sixes, then he must give them to you, and you get another turn and can ask again. If Bill doesn't have any sixes then he will tell you to "Go Fish" which means that you will draw one card from the pile on the table. If you get a six, then you show it to the other players and get to play again. If you get anything else you are finished with your turn and the player next to you plays.
If you have 4 of the same rank then you show the cards to the other players, and then place the four cards in a pile next to you. This is called a book. The player with the most books at the end of the game wins.
Drawing new cards
It can happen that you finish all the cards in your hand, either because someone else asked you for the last cards that you had, or you just got a book made up of your last four cards. If you have no cards then you can draw new cards from the pile on the table, the same number of cards as you got at the start of the game
If there are three or four players then it can happen that one of them finishes their cards and there are no cards left in the pile for him to draw. In that case he is out of the game and will simply have to wait while the remaining players finish the game.
Not much to say here. Just watch what the other players are asking for so you can know what cards they definitely have. If you're playing with more than two players make sure to pay attention to what the other players ask each other for and what they say Go Fish too, that way you can learn which cards they definitely have and which cards they definitely don't have.