The paper is pretty thorough and easy to follow. But if you want to the approximate version, as applies to most situations, it is as follows:
New Rating = Old Rating + k x ( Outcome - Expected Outcome) + Bonus term. k factor is a function of rating and number of games played. For a 1000 rated kid who has played 20 rated matches, k is on order of 55 - 65 I think. The Outcome is 1, 0, or 0.50. Expected outcome a function of the difference between the ratings of the 2 players: P(win) = 1 / ( 1 + 10^(-Rating Diff / 400 ).
philip
Who's Philip?