"Bring" implies moving or conveying something from a distant place or person to a nearer place or person. Example: Bring me a drink.
"Take" implies motion away from speaker to a person or place. Example: Please take me to your leader.
Some easy ways to remember the differences between "bring" and "take" are: You bring something here, and you take something there. You bring something toward a person, and you take something away from a person.
"Carry" implies the conveying of something from one place to another. Example: Please carry this to the car.
"Fetch" implies a two-way trip that is to go for something and bring it back. Example: Rover, fetch the ball.