The Elo system uses a rating and a K-Value to score players. When two players finish a match, the winner gains more points (up to the K-Value) if his or her rating is lower than the loser's, and less points if it's higher, and the loser loses that many points. How many points? Here's the formula:
If the higher rated player loses: Points = K-Value (1 / (1+10Rating Difference / 400))
If the higher rated player wins: Points = K-Value - K-Value (1 / (1+10Rating Difference / 400))
If both players have the same rating, the winner gains half the K-Value, and the loser loses the same amount.