Here's a basic guide to rugby that I have written myself. (with a little help from a marvelous little book I got at the NZ Maori vs. Canada game earlier in August)
Rugby is a game that is played with two teams made up of 15 players each and is played for 2 halves consisting of 40 minutes each half. Alternately, a version called Sevens is also played, with seven minutes each half and seven people per team.
The team is divided into backs and forwards. There are 7 backs (2 wings, fullback, scrumhalf/half back, flyhalf/first five eighths, outside center/center and inside center/second five eighths) and 8 forwards. (loosehead prop, tighthead prop, hooker, 2 locks/second row, 2 flankers/loosies, and number 8/loosie)
Typically the backs are smaller and faster than forwards, who are often bigger and stronger because they must win the ball in a scrum.
The match starts with a kickoff from one team and the reciving team tries to get the ball and move it downfield to score. The other team (usually!) tries to stop them and gain possession of the ball by tackling the player with the ball, also known as the ballcarrier. You cannot tackle a player without the ball. (unless you know the ref isn't looking)
Unlike American football, play doesn't stop after a tackle. The tackled player should try to put the ball backwards towards another teammate. However, as long as you are not coming from an offside position, the ball can be picked up by any player.
When players from both sides begin to fight for the ball when it is on the ground, this is known as a ruck.
A maul is the same as a ruck but the ball is kept off the ground and the players try to pry the ball from the ballcarrier.
If there is an infraction of the rules, (usually a knockon) or if the ball doesn't seem to be coming out of a ruck or maul, the referee will stop play. The play is restarted by a scrum. In a scrum, the eight forwards from each team bind together by grabbing eachother's shirts or shorts, etc. and push against eachother while the two hookers fight to get the ball and kick it back through their players. The ball is put into the scrum by a scrumhalf who also gets the ball out from the scrum and passes it out to the backs.
When the ball is moved downfield and and forced onto the ground over the opposing team's goal line, a try is scored. A try is worth 5 points. At this point, the team has an oppurtunity to earn another 2 points in a conversion. One of the players (usually the first or second five eighths) must kick the ball from the place it was scored (but backed up to about the 22 meter line) through the goalposts at the end of the pitch. The ball must not only go through the posts, but it must go over the cross bar as well.
There. Hope that was simple enough for people to understand...