Klondike is the most popular of all American Klondike Solitaire games. So much so, that in America, if you speak of 'Solitaire', you are almost certainly assumed to be speaking of Klondike, and most Americans don't even realize the proper name of Klondike, and call the game 'Solitaire'.
When playing Solitaire, the cards are dealt into 7 columns, with the last card dealt into each column face up. The column on the far left has a single card. The second column has 2, third column 3, and so on up to the seventh column which has seven cards in it. Cards can be moved between the columns, building the columns down while alternating suit (red on top of black, or black on top of red). The lowest card in a column will always be turned face up.
When the player finds an ace, he may use the card to start one of the four foundations above the tableau (7 columns). These foundations will be built up by suit during play. In other words, you can place a card onto the foundation pile, if it is of the same suit as the other cards in the foundation pile, and has a value one greater than the card that is currently on top of the foundation. The player wins when all the cards have been moved into these piles, and the top card in all four piles is a King.
The part of the pack that remains after the 7 columns are dealt is called the stock pile. You can deal cards from the stock pile into the discard pile by clicking on the stock pile. You may play the top card in the discard pile to either the tableau, or to the foundations. When you have dealt all the cards to the discard pile, you may click the area that once held the stock pile to recreate the stock pile from the cards in the discard pile, and begin to cycle through them again.