This skill is used in any situation where the character is riding on some kind of animal.
Overcome: Ride is the equivalent of Athletics when you’re on a mount - you use it to successfully accomplish movement in the face of difficult circumstances, like rough terrain, small amounts of clearance, or stunt riding. Obviously, Ride is also ripe for contests, especially chases, races and stunts.
Create an Advantage: You can use Ride to determine the best way to get somewhere on a mount, and a good enough roll might allow you to learn features of the route that get expressed as aspects, or declare that you know a Convenient Shortcut or something similar. You can also just read the Athletics description, and then make it about a mount. Advantages created using Ride often revolve around getting good positioning, doing a fancy maneuver (Did a Barrel Roll, anyone?), or putting your opponent in a bad spot.
Attack: Ride isn’t usually used as an attack skill (though stunts can certainly alter this). If you want to ram another mount, you can attack with Ride, but you take the same shifts of harm you inflict.
Defend: Avoiding damage to a mount in a physical conflict is one of the most common uses of Ride. You can also use it to defend against advantages being created against you or overcome actions of someone trying to move past you on a mount.