Not really that complicated. Sevens Rugby which you watched is a kind of an Arena Football Equivalent of "proper" 15 man rugby, used as a way to promote the sport by playing 2 or 3 day tournaments in places mostly where Rugby isn't that big (Dubai, LA, Las Vegas, Hong Kong and so on).
Real Rugby is 15 man a side, 8 forwards and 7 backs. The forwards main purpose on attack is to win line outs and scrums (they are the ones involved), do the majority of the work in the rucks (those big piles you see form at the end of every tackle) and provide tight defence near the fringes of play. They also carry the ball, but they usually aim to make hard tough metres up the guts. Backs are the runners and kickers, playing much wider and more loose. Obviously smaller and faster, but possessing all the skills.
A Try (same as a touchdown, except you actually have to control of the ball and touch it on the ground) is worth 5 points. After you score a try, you take a shot at goal for the conversion (2 points), but you must take the kick in line to where the try was scored. If the other team penalises you, you can take a shot at goal from where the infringement occured (this is worth 3 points). You can also score from a drop kick (a kick from the hand that must touch the ground, like that Flutie field goal for the Patriots in 05 or 06) which is also worth 3 points.
I'm rubbish at explaining things, but thats the basics I guess. The easiest way to learn is just to watch. At the moment, probably the second biggest event outside of the Rugby World Cup is occuring, the Lions tour. This is where the best players from the National teams of England, Scotland, Wales and Ireland are picked for the British and Ireland Lions, where they then tour one of South Africa (last in 2009, next in 2021), Australia (happening this year) and New Zealand (last in 2005, next in 2017). They only get together every 4 years, and each nation only gets a crack at them every 12 years so it's a big deal. The first test (of a three test series) was played last Saturday and was an absolute cracker, literally coming down to the last play of the game.
