This are blackjack rules made simple. It's a game played with one or more standard 52 card decks. All cards have their assigned value:
Ace = either 1 or 11, what is favorable for the person holding it
T, J, Q, K = 10
2-9 = face value
The objective is to get as close to total value of 21 with your cards without going over. If you go over you automatically lose.
Before the Deal
Before the deal everyone playing places a bet and any side bets. There is always a spread offered, so you can bet any amount between the table minimum and maximum.
Side bets are usually offered at casinos and you can bet on random events that could happen during a hand. For example betting whether someone is going to get two suited cards on the deal.
After everyone places their initial bet, the dealer deals two cards to each player face up and two cards to himself, one face up and one face down.
Players now have the option to do any of the following:
Stand - Take no more cards
Hit - Take another card. You can do this as long as you want until you either get 21 and win for sure or go over 21 and bust/lose
Double down - Double your inital bet and take exactly one more card
Split - If you have a paired hand, you can place another bet and split it into two hands. Now you are playing two hands and you decide for each one individually, if you would like to hit or stand.
Surrender - This is not possible everywhere, but some casinos do offer it. You can surrender your hand and take half of your bet back and lose the other half.
Some places there is also an offered side bet called insurence. It's offered when the dealer is showing an Ace and it has a 2:1 payout. You can bet a maximum of 1/2 of your original bet and in case the dealer has Blackjack, you win, but you lose your original bet anyway, so you basically break even.
After everyone has spoken the dealer turns around his face down card and adds cards to his hand until he either a total value of 17 or more.
Everyone at the table plays only against the dealer, so the four general outcomes are:
Player either has a value closer to 21 or the dealer went over 21 and busted. Either-way the player wins. Usually the payout is 1:1, so you get double your initial bet.
Player has Blackjack
Player won with a blackjack, that is you got exactly 21 on the deal. Payout for this is usually 2:3, so you get 1,5 of your initial bet profit.
Player either excceeds 21 and busts or has a lower value than the dealer. Either-way you lose your initial bet.
It's a push
The player and the dealer both have the same value. You get your bet back and a new hand is started. You are breakeven.
There are other variations of blackjack as well that mostly differ in payout structures, what counts as a puch and some other minor details that could have a big impact on the game. Make sure you check for any of these special rules before you start playing.