So you've sat down at a blackjack table and know the basics. Try to get as close to 21 as you can without going over. Hope to beat whatever the dealer gets. Got it.
But what about these other choices, beyond deciding how much to wager and whether to hit or stand? Where do they come in?
Doubling Down
Once you've placed a wager and received your first two cards, you're given a one-time option to increase your wager to twice the original amount and receive one more card to add to your hand. If you "double down" and don't like the third card you're dealt, too bad -- you must stand on that one additional card.
A good time to double down is when your first two cards add up to 11. Since there are many single cards worth 10 (all four of the tens, jacks, queens, and kings), your chances of making 21 with a single card are relatively good. Thus doubling your wager and agreeing to draw just one more card might well be a good strategy.
Splitting
While you can always double down no matter what your first two cards are, "splitting" can only be done if you're dealt two cards of the same value. That would include all pairs plus any two cards worth 10 (e.g., a jack and a king).
If you choose to split your hand, the dealer will separate your two original cards and deal two additional cards to go with them, treating them now as two separate hands. You're also asked to place an additional bet equivalent to your original wager on your second hand.
Let's say you're dealt a couple of sevens. You split them, and the dealer deals a king to go with one seven, and a six to go with the other. You're now playing two hands -- one currently worth 17 (the 7-K) and one worth 13 (the 7-6).
Splitting can be a good idea if you're dealt, say, a pair of eights (totaling 16). Since 16 can be an awkward amount to play (the worst, really), splitting and trying your luck with two hands containing an eight is often a better move. Meanwhile, splitting two cards worth 10 is a bad idea, since 20 is already a good hand on which to stand.
Incidentally, most casinos will also let you double down after splitting, and you can even split again if you're dealt a pair once more.
Surrendering
Another option is to "surrender" your hand. It is only after being dealt the first two cards that surrendering is an option, and by taking it the hand ends and you lose half of your original wager. Once you've hit or done anything else (e.g., doubled down), you can no longer surrender your hand.
Most players never surrender, which is similar to folding in poker except for the half-bet refund. In fact, it's only rarely a good strategy to surrender. One common use of the strategy is when a dealer turns out to have dealt himself a blackjack (making 21 with his first two cards). Since the player stands to lose anyway (unless he also has been dealt a blackjack hand), surrendering limits the amount lost.
It depends on the casino, though, whether this option is even available to the player. This is called the "early surrender" option, meaning a player is allowed to surrender right away after learning the dealer has blackjack. Otherwise, the dealer checks his hand to see he doesn't have blackjack, and only then are you given the option to "late surrender."
Taking Insurance
After the cards are dealt, if the dealer's up card happens to be an ace, the player is also given the option to "take insurance," which is like making a side bet on the hand.
Insurance allows you to bet up to half your original wager on whether or not the dealer has blackjack (that is, his down card is worth 10). If he doesn't, you lose your insurance bet and then proceed to play your hand as before. If he does, you win your insurance bet, but lose the bet on the hand -- unless you happen to have blackjack, too, in which case the hand is a "push." Thus if you take insurance for the full amount (half the original wager) and the dealer does have blackjack, you break even for the hand.
Generally speaking, taking insurance usually isn't a worthwhile play and beginning players should probably just decline the option. Even so, it is good to know what all of these other choices in blackjack are when playing, and to use them when circumstances suggest you should.