If you or the dealer is dealt an Ace and a ten-value card you have 21 known as a blackjack. This is a natural. If you get the blackjack you will be paid 3 to 2 for your bet providing the dealer does not get one at the same time. If you and the dealer have blackjack it is a push. If only the dealer has blackjack all players will lose.
To take a hit means that you want to draw another card. To signal the dealer for a hit you will tap the table in front of you or make a beckoning motion with your hand. If you wish another card after the first you would motion in the same manner.
Once you are satisfied with either your fist two cards or after hitting, you signal the dealer that you wish to stand. This is done by waving your hand over the top of your cards.
When you double down you are allowed to double your bet after receiving your fist two cards. You then receive one card only on your hand. Most casinos will allow you to double down on any two cards (DOA). Some casinos limit your doubling to hands that total ten or eleven. DOA is a favorable rule to the player. To signal that you are doubling down you will place an additional bet next to your original bet. Most casinos will let you double down for less than your original bet providing it meets the table minimum. This is foolish. You only double in favorable situations and it is to your advantage to double for the maximum.
If you are dealt a pair (two cards of the same rank) you can split these into two separate hands. You must make an additional bet equal to your starting bet. You signal the dealer that you are splitting by placing your second bet next to your first bet in the betting circle. Do not put this bet on top of the original bet. Do not separate the cards. The dealer will do this for you. You will no play each hand one at a time. The dealer will give you a second card to go with the first split card. You will then decide to hit or stand. After you play out this hand and stand you will move on to the next split card and the process will be repeated. Some casinos will allow you to double down on your first two cards after splitting. You would play this as you would if you were doubling down on your first two cards. This rule is favorable to the player.
If the dealer's up card is an ace the dealer will offer insurance. You are not really insuring a hand. This is a side bet you make wagering half your original bet that the dealer has a ten in the hole. If you make the bet and he has the ten you are paid 2 to 1. You would then lose your original bet but win the insurance bet, which works out to being a push of your original bet. If you have a blackjack and the dealer has an ace you will be asked if you would like even money for your blackjack instead of 3 to 2. If do not take the even money you will have a push if the dealer has a blackjack. Both the insurance and the even money bet are sucker bets. The dealers will NOT have a ten more times than they will have one.
Some casinos will allow you to surrender your hand and give up half your bet on your first two cards after the dealer checks for a blackjack. This is known as late surrender. This option is not offered in many casinos. It is to the player's advantage when played correctly. Unfortunately when it is offered many players surrender more hands than they should thus giving up the advantage gained by this option.