Blackjack has many rule variations, but the difference between most variations and standard blackjack rules are minimal. (With that said, small changes in rules can significantly change the house edge.)
Blackjack is played with 1-8 decks.
Cards from 2 to 10 are scored according to their face value, while jacks, queens and kings are scored as 10 and aces as either 1 or 11 (up to the player).
The goal in blackjack is to have a hand with a higher score than the dealer as long as the score is 21 or under. You don't compete against other players in blackjack, only the dealer.
When a player's hand score is exactly 21 with the first two cards, he/she has made a blackjack (meaning there has to be an ace and a face card or a ten). In standard blackjack games, players make 3:2 on their bet with a blackjack, which is why getting a blackjack is preferable for the player. There are 6:5 blackjack games too, in which making a blackjack pays 6:5 on players' bet and significantly increases the house edge when compared to standard 3:2 blackjack games.
You 'hit' when you want another card. A player can request more cards until his/her score is 21 or higher. In live games, you tap the table with your finger in case you want another card.
You 'stand' when you don't want any additional cards. The signal in live games is to wave your hand over your cards.
When 'doubling down', you double your bet and receive exactly one more card. After having doubled down, you won't be able to request additional cards. You can only double down with the first two cards (so if you've been dealt three cards, you can't double down anymore). The signal in live games is to place another bet next to your original bet.
You can 'split' when you have two cards of the same value, such as two 6's. The sixes become separate hands and both hands are automatically dealt additional cards, so that there'll be two cards in both hands. You'll have to place an additional bet since you now have two blackjack hands to play. The value of the additional bet must be equal to the original bet. You'll be able to either 'hit' or 'stand' in both of the hands. In some games, you'll be allowed to double down after having 'split' your hand.
You'll only be able to 'surrender' in some games. The act of surrendering in blackjack means that you you receive half of your bet back and give up the current hand.
Dealers have no options in blackjack.
They only have a simple rule to follow. They must take more cards until they reach a score of 17 or higher, after which they must stop taking more cards. (Remember that aces or 1 or 11 for the dealer, too, so even if the dealer reaches 17, for instance, with an ace and a six, he/she is allowed to take more cards in case you have a score higher than 17, since the dealer just decides to play the ace as 1.)
1. Players bet:
Players have to place their bets before the game starts.
2. First cards are dealt:
Once players have placed their bets, the dealer deals two cards per player. Cards are dealt one per round, so the dealer makes two rounds. In shoe games, players get their cards dealt face-up, while in hand-held games they're dealt face-down. One of the dealer's cards is dealt face-up, one face-down.
3. Players' turn:
After the first two cards have been dealt, the players got options which have been explained above.
4. The dealer's turn:
After all the players have made their decisions, it's the dealer's turn to act unless all the players have already busted, in which case the dealer automatically wins.
You can win at blackjack by having a higher score than the dealer up to 21.
You can lose at blackjack by having a lower score than the dealer.
You can also lose by having a score higher than 21, in which case you "bust".
If both the player and the dealer have equal scores, the player receives his bet back.