Basics of CA:
A - CA for your cards.
-1 for a card that leaves your hand.
+1 for a card that enters your hand
-1 for a card that leaves play.
+1 for a card that enters play.
Meaning that, normally, playing a permanent costs you no CA. Losing a permanent costs you -1 CA. Playing an instant or sorcery is -1 CA in this part. Normally, however, your instants and sorceries provide you with some sort of CA from part B.
B - Your opponents' effects on you.
+1 for a card that leaves your opponents hand.
-1 for a card that enters your opponents hand.
+1 for a card that leaves play for your opponent.
-1 for a card that enters play for your opponent.
Meaning that destroying your opponent's permanents or their hand gains you CA, while letting them draw *cough*Arcane Denial*cough* loses you CA.
C - Special cases
Tokens - What Oscar Tan and Georgie Tait disagreed about. Rasko says that tokens should be counted as cards in terms of counting CA, while Tait says that you shouldn't. I say that you should, except in special cases like Decree of Justice (Decree for 4? I get +4 CA? Not really).
Note that this has NO effect whatsoever on Tempo, which is a less concrete concept. Maybe I'll try to explain that in more detail later.