The Chess Rating system used by FIDE, since 1970, is based on a system modified by Hungarian physicist, Arpad Elo (right), which retains his name: the "Elo Rating System".
At the very basic level, in order to avoid doing complex maths, you just need to know that scoring, per game, gets the following:
For those who like to suck up the details - including formulas used, these two links should gratify your obsessive mind:
Elo Modifies The Harkness System
The Elo Chess Rating system wasn't the first - published in 1956, "The Harkness System", created by Kenneth Harkness, was already in use by the USCF (United States Chess Federation) for over two decades ...
However, according to the ChessBase article (Arpad Elo and the Elo Rating System), there were some shortcomings that produced inaccurate results.
Rather than creating a new system from scratch, Arpad Elo kept fundamental aspects of the Harkness System - the Rating Scale and the Class Categories of that scale - and modified the rest.
The Elo Rating system was approved by the USCF in 1960, although not everyone was satisfied with it, in particular, a chap called Sam Sloan, who favored the Harkness system for it's potential to allow a more-rapid rise up the rankings.
You can read Sam Sloan's article/rant here (WARNING: the guy's gone and put some dodgy audio file on his page, which plays as soon as the page is loaded - you'll find the player at the bottom of the page).
Anyway, the Elo System was finally adopted by FIDE in 1970, for use in its global tournaments.
Doing Things Differently
Because of the endorsement by FIDE, these guys being the World Governing body of Chess, you'd think it'd be most sensible for all other Chess federations to follow FIDE's ranking formula ...
Take football, for instance ... FIFA are the World Governing body of this sport and all the way down to the 'grassroots' level - the amateur Saturday/Sunday league clubs - the same rules are followed: 3 points for a win, 1 for a draw, 0 for a loss.
At the end of the 90 minute match (96 minutes, if you Man Utd, playing at Old Trafford), regardless of whether a result seemed deserved or not, everybody can determine the points gained - or not, for a loss - and how that reflects the overall Rankings ...
However, when it comes to Chess, you can find differing interpretations, resulting in different points scored, for the same player ...
Wikipedia's article, on the Elo Chess Rating System, makes the point with an example, within the section about Different Chess Rating Systems: "someone with a FIDE rating of 2500 will generally have a USCF rating near 2600 and an ICC rating in the range of 2500 to 3100."
Besides Harkness and Elo, there have been other Chess Rating systems used, and you can read about them via the following links: