When card counting do you count the other cards from players at the table too?

ok so I understand the basis of card counting and the +/- number system but here is my question ... when counting are you also able to count the cards of the other players at the table or is it strictly between you and the dealer? (now this is where my blackjack question comes into play) so i have never played blackjack at a casino so i am unsure how it works, but when you are dealt, the first card is down while the second is up for all to see. So when does the first card get flipped? when you start to hit or stand etc and is this when you are able to count the cards else where on the table from other players?