Go play against some really people. Their repeated recommendations of sucking tons of dicks and uninstalling the game will give you all you need to know about team cooperation.
No, but seriously, if you really want to get into it, pick a single character that you like, and play that one constantly. Look up an item purchase order online, and a strategy guide or two. Remember that not dying is more important than anything else. Don't kill yourself trying to save a tower - you'll die, and they'll take down the tower anyways. Don't kill yourself trying to destroy a tower, or a player. Those might be risks you can take when you know the game, but for now you'll be doing your team a bigger favor by feeding as little as possible. I'm no expert on the format, but I know that much. You will probably not be decent before you've put 40-50 hours into it.