Procedure question
 

When a player is cautioned the second time he/she also earns a red card. What is the proper procedure for NFHS and USSF?

Do you call the foul, then sequentially show the (2nd) yellow, then show the red? Or do you show both the (2nd) yellow and red together at the same time?

First, you need to blow the play dead (whistle). A delayed red card is very risky and might easily blow up in your face.

For FIFA, you show first the yellow, and then the red. I believe US high school is the second example, but am not the best person to answer.

BCer is correct.
In USSF which follows the FIFA Laws of the Game, with some minor alterations, the referee would 1. whistle and indicate the foul 2. isolate the offending player and administer the caution 3. display the red card after putting away the yellow and send the player off. This team now plays a man short for the rest of the match.

The NFHS rules are vastly different. The procedure is the same for steps 1 and 2. However, in step three the referee displays BOTH the yellow and red cards together in ONE hand. This indicates a soft red card. The player is disqualified, but the team is allowed to replace him and continue the contest with the same number of players as before the offense.