PROTIPS FOR NEW CARC PLAYERS
-You can play an unlimited amount of friend games at one time.
-All friend games are asynchronous so whenever it's your turn you'll get a notification or you can go to the games menu to see the badges so you know where your game is at.
-To get to the Games menu from the home screen go to Normal Game --> Resume Game.
-To get to the Games menu from a game hit the Gear icon then Pause (this doesn't actually "pause" anything since the games are always "paused" in the sense that they are asynchronous; it just takes you to the menu).
-The games menu will show you both your current invitations (sent & received) and your current games.
-Received Invitations: To join a game, simply click on it under your invitations. You can then "reject" the invite if you wish or just stay there and wait for it to start otherwise (you don't actually have to literally wait there -- ASYNCHRONOUS!)
-Sending Invitations: Normal Game --> Internet --> Play with Friends. Add via either email or from your current friends list. Note that you need an email address to add someone and can't just add by username. Note also you can start a game before everyone has arrived if you don't want to wait. It will just kick them out of the game.
-Badges: There are little badges next to each game. The wood-colored one means new activity such as a turn or someone joining. The green one means it's your turn.
-Notifications: You should also get alerts even out of game when it is your turn or when you've been invited (but check the Games menu periodically just in case).
-Internet Quickplay: Been a while but I'm pretty sure this is still 2p-only and not asynchronous. Friends is pretty much the way to go unless you want the more hardcore competition.
-Rules: If you need a refresher here is the pretty Rio Grande manual:
http://www.riograndegames.com/uploads/Game/Game_48_gameRules.pdf.
EDIT:
-Timing: Play games at your leisure. Some games take a day, some take a week. Try to get in at least a turn or two a day if you can but that's about it (the more turns the better though of course!)
-Chat: After other players have seen the final score and exited the game, they can no longer see the chat even if you still type in it.
Think that's most of the basics, let me know if you have any questions.