You can find Hipparchikos and Peri hippike online in English at the Perseus Project.
The first duty of a cavalry commander, says Xenophon, is to sacrifice to the gods. Then you must recruit, see to it that the horses are properly taken care of, and train and arm your men. You should have high standards, focusing on excellence of horsemanship, and if you do this will actually inspire young men to join you. He gives a number of practical tips on all of these things, including formations.
Having talked about the general matters, he passes to talking about what a cavalry commander himself must first do. His first duty is to fulfill his religious responsibilities, making the sacrifices to the gods for the cavalry, participating in the religious festivals, and the like. He gives some tips on the best way to do these things. In Chapter 4, we learn how to handle a march and how to position oneself to have an advantage over the enemy. In Chapter 5, he covers the things a cavalry commander must be able easily to estimate -- how quickly a horse can catch a man on foot or another horse, as well as the best tactic to use against an opponent doing different things. These estimations require a great deal of experience with horses, and close attention to their condition under different circumstances. A cavalry commander also has a responsibility to make sure that the city understands that a cavalry needs an effective infantry if it is itself to be fully effective. (Given Greek weaponry, cavalry was highly vulnerable to infantry attack, and so needed a counter-infantry for defense.)
Xenophon then talks about the importance of morale and moral authority; the men need to think of their officers as wiser than they are and worthy of respect. Cultivating loyalty requires kindness and, just as important, care for men in the practical sense of making sure they are properly fed and equipped, as well as letting them share any benefits the officers themselves might have. The basic rule is straightforward: "To put it shortly, a commander is least likely to incur the contempt of his men if he shows himself more capable than they of doing whatever he requires of them" (6.4). And, of course, Xenophon notes the most important thing to getting the loyalty of your men: they need to be confident that if they obey you they will not needlessly die. The commander must exercise prudence.
All of this is especially important to the Athenians, who are surrounded by cities that also have good cavalry and also are capable of fielding large armies. This guarantees that the cavalry commander will sometimes be required to enter hostile territory under less than ideal conditions, and he needs to be ready to handle such situations.
The key to handling battle is training, training, training; your men must be so good at handling a horse that it comes practically naturally. The horses, too, must be properly trained, fed, and exercised, so that they will respond optimally. (In an interesting comment, he notes that training in horsemanship is pleasant work, because it is the closest a human being can ever get to flying.) He notes some common errors in the use of cavalry that men need to be trained against.
The final chapter notes that it is impossible to cover everything required for cavalry command in a single treatise:
To read these suggestions a few times is enough; but it is always necessary for the commander to hit on the right thing at the right moment, to think of the present situation and to carry out what is expedient in view of it. To write out all that he ought to do is no more possible than to know everything that is going to happen. The most important of all my hints, I think, is this: Whatever you decide to be best, see that it gets done. Whether you are a farmer, a skipper or a commander, sound decisions bear no fruit unless you see to it that, with heaven's help, they are duly carried out. (9.1-2)
He makes some additional comments on raising a cavalry force and ends the work by reiterating the importance of piety to the gods:
All these things are feasible provided the gods give their consent. If anyone is surprised at my frequent repetition of the exhortation to work with God, I can assure him that his surprise will diminish, if he is often in peril, and if he considers that in time of war foemen plot and counterplot, but seldom know what will come of their plots. Therefore there is none other that can give counsel in such a case but the gods. They know all things, and warn whomsoever they will in sacrifices, in omens, in voices, and in dreams. And we may suppose that they are more ready to counsel those who not only ask what they ought to do in the hour of need, but also serve the gods in the days of their prosperity with all their might. (9.7-9)
The treatise on the correct method of handling horses opens, naturally enough, with advice on how not to get cheated in buying a horse. He chooses not to discuss the breaking of horses, because riding is far more important to cavalry -- certainly young men should focus on riding, and leave breaking horses to their elders. Nonetheless, a horseman must take care that the one who breaks in a colt does his job properly. He then moves on, in chapter 4, to discuss how to take care of horses, by having a proper stable, food, and cleaning procedures, and taking appropriate thought to their hooves. The horseman must also make sure his groom knows what he is doing (Chapter 5).
After a number of other tips on the care of horses, Xenophon turns to advice on riding. Riding he sees as pedagogical in character: the rider must teach his horse. The art of horsemanship is a teaching art:
Now, whereas the gods have given to men the power of instructing one another in their duty by word of mouth, it is obvious that you can teach a horse nothing by word of mouth. If, however, you reward him when he behaves as you wish, and punish him when he is disobedient, he will best learn to do his duty. This rule can be stated in few words, but is applies to the whole art of horsemanship. He will receive the bit, for example, more willingly if something good happens to him as soon as he takes it. He will also leap over and jump out of anything, and perform all his actions duly if he can expect a rest as soon as he has done what is required of him. (8.13-14)
Since horsemanship is a form of teaching, it requires taking into consideration the character of the horse. Like human beings, horses have thymos, spirit or drive, and thus it is possible that you have a very spirited horse, and handling a spirited horse is exactly like handling a spirited man -- you avoid unnecessarily annoying him, and focus on gentle guidance. He vehemently rejects any thought of trying to handle the spirited horse by tiring him out -- by its very nature a spirited horse will take this as a challenge, and will likely harm himself trying to do more than he can do. Like a spirited man, a spirited horse likes victory; he must be held back by the rider from running his top speed or racing other horses, because he will not hold himself back if he is given a challenge. Likewise, the rider himself must remain calm, or the horse will get too excited. But, says Xenophon, if you are going to war, it's probably best to avoid spirited horses. If the horse is not spirited but sluggish, however, you must do everything in exactly the opposite way.
Xenophon then sharply criticizes common practices when it comes to displaying horses. If you want to show off a horse, you have to teach him in such a way that he likes to show off: "But if you teach the horse to go with a slack bridle, to hold his neck up and to arch it towards the head, you will cause the horse to do the very things in which he himself delights and takes the greatest pleasure" (10.3). He gives some tips on how to do this, but notes that only particular kinds of horses are good for parade: they need to be strong and spirited. The key principle in all of this is that horses are most beautiful and graceful when they are not coerced, so the rider has to develop a sense of how to guide the horse without making the horse feel like it's being forced to do something.
The last chapter ends with a discussion of how man and horse should be armed for battle, but ends by noting that all his comments in this work are for the private person, not cavalry commanders, and refers the reader to the appropriate treatise for that subject.
The astute reader will note that Xenophon's treatise on cavalry command is structured so as to be also a treatise on leadership, and his treatise on horsemanship is structured so as also to be a treatise on teaching, just as his treatise on hunting with dogs was structured so as also to be a treatise on learning how to be virtuous. This is a typically Xenophontic theme. Each specific domain has its own quirks, but they all require certain general virtues. The prudent person will understand how to take the specific case and properly generalize it.
Quotations are from the Marchant translation at the Perseus Project.