Blackjack counting systems really started to emerge in the 1960's in America. The game of Blackjack was really catching fire—thanks to the new books on the subject in the last 1950's. The entire mathematics side was exposed and people started to realize that they could make serious money playing Blackjack if they knew what cards were left. In those days, it was all about the single deck game. Today, single deck games are tougher to find and usually are reserved for people playing at least $25 per hand.
Counting cards in Blackjack is not about knowing the exact cards that remained—like the seven of clubs. Rather, when you card count, you are just trying to figure out what "type" of cards remain. When you count cards, your main goal is to figure out if the remaining deck is full of big or small cards. Small cards heavily favor the dealer while larger cards favor you getting a solid hand.
Entire teams were setup in years past to simply control a table and beat up on Blackjack by counting cards and altering bets. The altering of bets is an important move. When the deck has mainly smaller cards remaining the counter will lower his or her bet. The counter will wait for the deck to be adequately stocked with larger cards before placing a large bet.
Card counting systems run from extremely basic to mathematically complex. The simplest systems are designed to be easy to use and to give the counter a general idea of what's remaining in the deck. Some cards in simple systems aren't counted. In more complex systems, each card is given a specific "count" and the percentage of cards played and remaining are factored into the count as well.
What follows is an extremely basic card counting system.
Card: 2 or 3 Count: +2
Card: 4 or 5 Count: +1
Card: 6 or 7 Count: 0
Card: 8 or 9 Count: -1
Card: 10, Face or Ace Count: -2
As you see each card listed above, you add or subtract to your running count. Your count for this simple system starts at 0 for each new deck. The higher your count goes, the more the deck favors you getting a good hand. If you are playing a multiple deck game, the count needs to higher before you jump in with a large bet, because the number of cards being used are greater.