Your hand will only consist of 3 cards. You would now be playing 2 separate hands, each starting with one of the two split cards. A new wager equal to the initial wager must be placed for each split hand. You will then be dealt a second card to one of the hands. After this hand is played out, the second hand will be dealt a second card and continued until that hand is played out.
All regular rules apply to each hand with the ability to double down or split.
If the dealer's first card is an Ace, there is a possibility that he may have a Black Jack. The player can, if he believes the dealer's hidden card is a 10 or face card, insure himself against Black Jack. If you choose to accept insurance you have to pay an amount equal to half of your original bet. Therefore, insurance is to be considered a game of its own within Black Jack, and it gives the player a chance to protect himself, when he thinks that the dealer has Black Jack. Players win their wager if their total hand is higher than the dealer's without going over 21.