The most important thing to know about blackjack is the basic strategy. This strategy is simply the best way to play every possible situation, without any knowledge of the distribution of the rest of the cards in the deck. At the top of the page is the basic strategy for four or more decks when the dealer hits on soft 17, which is the most common game. Below are links to more basic strategy charts for other rules. If you only memorize one table I would suggest the one above. It can be played effectively under any rules.
To use the basic strategy look up your hand along the left vertical edge and the dealer`s up card along the top. In both cases an A stands for ace. From top to bottom are the hard totals, soft totals, and splittable hands. Rule variations can have an effect on some borderline situations. The most flexible rules are the number of decks, whether the dealer hits or stands on a soft 17, and whether doubling is allowed after splitting.
Some obvious situations have been left out to keep the chart as small as possible. I have more basic strategy charts for other numbers of decks, as well as European blackjack.
deck
decks
or more decks
European blackjack
The best way, I have found, to memorize the basic strategy is notice patterns and to try to understand why you should play every situation as the chart says. Then make flash cards and go over and over them until you know it cold. Do not deal out cards to yourself because the soft totals and the pairs will not occur often enough to test your knowledge.
Many people do not believe in the basic strategy because they once took the advice of someone who knew it and then lost the hand. Let me make something perfectly clear, you will not win every hand with the basic strategy! In fact, you won`t even win half your hands. However, I can personally testify that while you will have short term ups and downs, over the long run you will roughly break even using it.