The early stages of training a Thoroughbred race horse are not much different than training any other horse. They start by being halter trained, this progresses into ground work, then finally finishes with conditioning and track work. The race horse industry has professional trainers that handle preparing a horse for the track.
Halter training is usually done early while the foal is still with its dam. They learn how to walk, trot, and halt while on a lead. They also learn how to accept being handled and having their feet picked up and touched. These foals are taught to tie, and be "sacked out" this means they are taught to allow scary things (blankets and such) to touch them without jumping away. Then they are left for a while to grow up. At a year of age the owner, and his trainer, may have a look at them picking out which they think are suited for racing, this will be based on pedigree, development, attitude, and conformation. These reviews may occur many times before training begins. Usually though, the bulk of training starts late in a horses yearling year. Note: Thoroughbred horses are giving the artificial birth date of January 1 of the year they were born regardless of the actual year.
As late yearlings they are taught ground work, which first reviews all halter training, and then introduces lunging. Lunging is where a horse proceeds in a circle at the end of a long "lunge line". The trainer uses voice commands (and the sound of a lunge whip) to indicate to the horse what speed it should be going). Lunging starts getting the horse into shape for further work to come, and allows a controlled setting to introduce the bridle and saddle. For the record, most other breeds of horses are not trained to this point, at this age, but are usually given another year or two to grow up and mature.
Later the young Thoroughbred horse is "ground driven". By this we refer to the horse being bridled with two long reins from the bit, through a surcingle around the horses middle, to the trainer who is walking behind, and slightly off to the side. Now the horse learns to respond to the bit for control.
When the horse is responsive to all it has learned, a rider, usually a light weight person, will mount it for the first time. With one person holding the horse, the other will only drape themselves over the back of the horse at first, sitting up if they are confident the horse will not react unfavorably. If all the ground work has been done well, this is usually an easy process, as the horse trusts its handler.
From here on training progresses with a "conditioning" factor. It is not enough for a young horse, who may be racing in only a few months, to just accept a rider, they must be in condition to race. Sometimes trainers will back off a horse and leave it until its third year to race, but many are pressured by the owners to get them onto the track at two years of age.
Remember the horse still is not at the race track, it is still on the trainers property. Most trainers do have a false track set up and exercise the horses there with the company of other horses, or alone. Some conditioning exercise consists of a rider on an older experienced horse leading around the younger one. This is called "ponying". A lot of conditioning is done this way at the trot. Other conditioning is done by the use of putting the horse on a "hot walker", a piece of equipment a horse will probably spend a lot of time on once at the track, so it must be trained how to walk in a circle with the help of a machine.
The Thoroughbred must be taught how to change their leads, because for a horse to race on the same lead for the whole time is very difficult, typically they change their leads just before and just after a turn. The training would be done at a canter first, then at a gallop.
Finally the horse is introduced to the starting gate. It should be pointed out here that not all countries use starting gates, but for those that do, the trainers must get the horse used to the tight space and the sound of the starter bell. Sometimes this is done at home, other times this is done first at the race track. Some trainers have old disabled gates at home and walk the horses through them on the way to the pasture so they do not get nervous when they first encounter the starting gate.
At the track the training continues but is now monitored and reported as "workouts" by the horse race forms, so that the public who may wish to bet on these first time starters have something to compare them with.
A horse who has never won a race before is referred to as a maiden. They are unproven and full of unknowns. Hopefully the trainer and owner made the right choices in selection, and provided the right training, for the horse to have a long and successful career.