Promotion
The basic move of the pawn leaves a rather large hole, which I hope you at least wondered about. What happens when a pawn reaches the far side of the board and there is nowhere else to go? Since a pawn can't move sideways or backward, what use is it?

When you are ready to promote a pawn and there are no queens available, you can usually get a hold of a captured rook and turn it upside down. If none are available, you can place two pawns on the square or turn a piece or pawn on its side. There is always a way!
This is where promotion comes in. Any pawn, upon reaching the farthest possible rank (the eighth rank for White pawns and the first rank for Black pawns) undergoes a metamorphosis. You remove the pawn from the board and replace it with a piece.
Promotion, by the way, has nothing whatsoever to do with any of the pieces already on the board, or even with any of the pieces captured. A pawn upon promoting theoretically turns into whatever piece you want it to turn into.
Practically speaking, this doesn't happen, of course. Instead, you must search among captured pieces or get a hold of another set in order to make a second or third queen, for instance. If nothing is available, however, you'll find a way.
A New Quenn
You always have a choice as to which piece you want to turn the pawn into. But first consider the restrictions: The pawn cannot remain a pawn, and it cannot become a king. Nor can it become an enemy piece (not that you'd even want to make it into one!).
This choice is most often not thought about at all. The queen is such a powerful piece that almost every pawn that is promoted is promoted into a queen. In fact, this is often called queening the pawn.
White is poised to promote the pawn. Remember that White pawns move up the board, while Black pawns travel down the board.
White has turned the little pawn into a queen. This is a rule that made it into Lewis Carroll's Through the Looking Glass.
Underpromotion
Nevertheless, there are times when you might not want a queen. In these cases, it's good to know that the choice is yours. You can promote to a rook, a bishop, or a knight, as well as a queen. As for why you might want to do such a ridiculous-seeming thing, a very simple example will suffice.
White's pawn is ready to promote. Should it become a queen?
Look at the diagram. You are White and it is your move. If you promote the pawn to a queen your opponent will then checkmate you and you will lose. If, however, you underpromote the pawn to a knight, it is checkmate and you win!
White has decided that greedily promoting to a queen and losing is not the way to go. Underpromotion to a knight produces this checkmate.
Just keep in mind that the choice is yours every time you promote a pawn, and the choice is your opponent's every time she promotes one of her pawns.
Promotion with a Capture
One of the most spectacular changes you can bring about during a chess game is to capture a piece, let's say the opponent's queen, with a pawn while promoting it to a queen. To gain two queens in one move is unbelievable, but it is actually possible.
Black has a pawn for a queen. But it is Black's move, and Black pawns march downward.
In one move Black has transformed her pawn into a queen while capturing the White queen.

