[RPG] the process to train an exotic (aerial) creature to be a mount

A mount must be at least one size larger than the rider. So a medium rider requires a large mount. In addition, a flying mount can only fly with a rider that's within the mounts light load. (DMG 204)

For general purpose riding, training is generally not required. No Ride checks are required either, though if the animal is actively unwilling to bear a rider than your DM can require a Handle Animal check (a wild Dire Bear is probably not just going to let you hop on!).

Typical riding actions don’t require checks. You can saddle, mount, ride, and dismount from a mount without a problem.

For combat riding, things change and a Ride check is required if untrained:

As a move action, you can attempt to control a light horse, pony, heavy horse, or other mount not trained for combat riding while in battle. If you fail the Ride check, you can do nothing else in that round. You do not need to roll for warhorses or warponies.

Thus, combat riding training is required both to avoid the check, and to avoid using a move action to make the check.

If your animal is tame, then you can ride it. In the Ride skill description, it says about riding animals:

When reared from birth, the following animals can easily be ridden by Small or Medium humanoids, depending on the riding animal's size.

This heavily implies to me that you can ride tame animals regardless of what tricks they know through Handle Animal. However, without knowing tricks, the animal will be very difficult to use practically. You will likely need to make ride checks to control your mount in combat if it hasn't been trained in combat, and you will need a DC 25 Handle Animal check to make it do anything that it hasn't been trained to do already.

You can mount a tame lion that knows Come and Stay, but it will be difficult to bring it into combat, and you won't be able to have it walk alongside you without a DC 25 Handle Animal check.