What age should I start training my young horse?

You can start training your young horse or foal practically from the moment it is born.
Imprint training the new born foal can be very beneficial, providing it is done correctly.

The age you actually start breaking in and riding the horse will depend on a lot of factors.
Including the horses breed, what sort of riding you want to do, the horses individual maturity, and how big you are compared to the size of the horse.

Race horses are started very young and are racing at only two years old.

Unfortunately, young horses bones have not finished growing at this age, and such strenuous pressure exerted on young tendons, joints and ligaments frequently means that few two year old race horses stay sound enough to have long careers after they have finished racing.

Most horses can be safely started at two to three years old. Providing they are only worked lightly and not forced to work over jumps, in heavy sand, rough terrain, tight circles or for long periods.

Large horses such as warmbloods, andalusians as well as cold bloods and draft breeds tend to be very slow at maturing. Their joints are still open and don't really close until they are four or five. For this reason it is better to wait until these bigger breeds are at least three before they are started. Even then they should not really commence heavy work until they are five or six years old.

Horses don't stop growing until they are about seven years old.

At around six years old the horse will start filling out more and bulking up in the shoulders and hindquarters. This is when the horse is strong enough to carry a rider and perform without causing slow deterioration of joints.

However there is soooooo much you can do with your young horse that does not involve riding.
There is no reason why you cannot do heaps of desensitizing and training responses to all the basic pressure cues before you ever even put a saddle on their back, let alone a rider.

This will all make the horse safer, calmer and quieter when you do actually take that first ride.