I would like to add to Lord Brawl's most excellent writeup of what is in my opinion, they best casino game out there. (With poker a close second, but that must be with 5 people around a table at someones house, with strict rules enforced)

When cards are played in blackjack, they are discarded until the deck runs out. Then the dead pile is reshuffled, cut, and dealt from as usual.

In Blackjack, when you have two identical cards, you may split them into two seperate hands. This is done by physically splitting the cards, and matching your initial bet. You then play each hand against the dealer as you would any other hand. It is not advisable to split hands which would total above 17, unless you have been counting cards, and know what is in the deck.

Double Down is when you match your initial bet, declare double down, and the dealer deals you another card face down. This is then the hand that you play with. Some casinos restrict when you can double down, like to hands totalling 10 or 11 only, or after a split. The less restrictions the better. Doubling down on something like 14 or 15 is generally a good bet if you can have an idea that you aren't going to bust. Unless you get a 2 or and ace you are going to beat the dealers stop point.