As the others have pointed out, everything you remember about competetive Magic is still around, and more so.If you last played 7 years ago then that was around the time of Ravnica, so as luck would have it, this fall's new block is "Return to Ravnica."
Since then, there have been a number of rules changes. The more significant ones include:
1) Damage no longer uses the stack. You can't block with Mogg Fanatic, put its one power worth of damage on the stack, and then sacrifice him to deal one more damage from his ability. A lot of whining was heard but its been just fine.
2) No more mana burn. They claimed it was an outdated rules interaction and that eliminating it would open up more design space. Haven't quite seen all of the new things they can do with it gone but in all reality, it hasn't been missed much either.
3) Not really a rules change, but there's a new card type called "Planeswalkers." They've generally been the most powerful things you can do in a game and are almost always the most expensive cards in the set. Read up on the rules about how to use them and play with and against them.
Since the rotation is about to happen, beginning in October the cards from Innistrad, Dark Ascension, Avacyn Restored, Magic 2013 and the new Return to Ravnica will be legal. Read up on those sets and check out the mechanics. Morbid, Miracle, the Transform cards, and more.
As for actual tournament Magic, you're in for a treat. There has been a boom in options. Wizards tightened up on the Pro Tours, there are only 3 each year plus one new World Magic Cup type thing. No need to worry about that just yet. They are invite only which means you have to win a PTQ, or Top 4 a Grand Prix, or have points from the Pro Players club or Hall of Fame to go.
Luckily, they've nearly doubled the number of Grand Prix each year and there's almost one every week. Obviously not all in the US but still. There's a ton.
In addition to all that, there's a number of independent tournaments that have gotten quite popular as well. The biggest is the StarCityGames Open Series. Again, almost every week they have a tournament in a new city. On Saturdays they have Standard and on Sunday's they have Legacy. They pay out quite a bit (more than old Grand Prixs used to) and have their own points system for your wins that can get you invited to their invitational tournament for more money and prizes.
There's a few others like TCG Player (though I think that's mostly a midwest thing) and I'm sure there's something out west. It shouldn't be too hard to find.
Start by going to an FNM locally and I'm sure the players will glad to help out more.