It happens more often than I'd like to admit: my ball ends up on the cart path.
To take relief from a cart path, or any immovable obstruction, you first must establish the nearest point of relief without going closer to the hole. For a cart path, go to one end of the path and mark where you are free from the relief. Then, go to the other side of the path and establish where you are free from the obstruction. Put a mark there.
Free from the obstruction means that both you and the ball are off the cart path.
Once you have two points marked, you must decide which of the two points is closer to the ball on the path. After you make that decision, you have one club length from the mark where you are allowed to drop your ball.
Remember, just because there are two marks, you are not allowed to decide which point is best. You have to take the one closest to the ball.