A golf course without cart paths is a rarity.
Knowing your rights is a necessity.
First, a player is entitled to relief from the cart path in any of these situations: 1) the ball is in contact with the cart path, 2) a player’s normal stance is in contact with the cart path, or 3) the player’s swing is interfered with by the cart path (e.g. the ball is resting close enough to the edge of the path that the club head will contact the path during the swing).
Second, relief from the cart path is an “entitlement” not a “requirement.” If for some reason a player prefers not to seek relief from the cart path, they may play the ball as it lays.
Third, here is how we go about determining our relief: 1) leave the ball (temporarily) where you found it. Then, 1) Use a marker (coin or tee) to identify the nearest point (no closer to the hole) the ball could be placed where the cart path no longer interferes with your swing and stance. 2) Holding the ball at knee height the player must drop the ball at this point or any point within a club’s length of this point (no closer to the hole). 3) As long as the dropped ball does not roll more than two club lengths, does not roll closer to the hole, nor rolls back onto the cart path, the ball is now in play.
Remember the above and you’ll be on the right path to handle the cart path.
note: Obstructions and relief are addressed in rule 24 of the USGA’s Rules of Golf. These are expanded upon in the USGA’s Decision on The Rules of Golf page 386. If you consult the Decisions, be advised that the diagram on page 386 is misprinted with the points printed 5 mm too far to the left.