Instructions
Booting from Games
Wait for a player in your party to betray you and kill you. This can happen either on purpose, such as them actually shooting at you, or accidentally, such as a rogue grenade. After they've done it a few times, a "Boot Player" screen should pop up.
Press "X" to boot them from both the game and your party. (You can also choose "B" to forgive the player and let them stay.)
Wait for the connection to reset. This will stop the game for a few seconds as the booted player is removed from the game.
In Between Games
Press the Xbox "Guide" button, which is the button in the center of your controller with the Xbox logo.
Scroll down and select "Party."
Scroll down and select the player you wish to kick from your party.
Select "Kick from Party." The player will be removed from your Xbox Live party. However, they can still request to rejoin.