How to Make a Horse Stop Rearing while Riding
To make your horse stop rearing while riding, loosen its reins, since tightening them will only make it rear more. Make sure you stay in the center of the saddle so you don't loose your balance as its rearing. If you think your horse will rear again, tighten your grip on 1 of the reins and pull it out to the side to lead your horse into a turn. This will keep your horse from rearing until it has the chance to calm down. To prevent rearing in the future, try working on your horse's groundwork. To do this, retrain it to step back by giving it light taps on its shins with a long whip. When it steps back, reward the behavior with treats and verbal praise.
Loosen the reins. If your horse starts to rear, the first thing you should do is loosen the reins. This may seem counterintuitive, as your gut reaction will probably be to pull, but this will only make things worse. Continue to maintain your grip on the reins. In other words, don't just let go or loosen your grip. Push your hands towards the horse's mouth while holding firmly onto the reins to loosen them up. Never pull back when the horse starts to rear. This may cause the horse to rear further, potentially flipping the horse over on top of you. Stay in the center of the saddle. While loosening the reins, make sure you remain centered in the saddle. This will help you keep your balance as the horse rears and flails. You may be tempted to lean with the horse or to try and lean around whatever it's afraid of (if there's something on the trail). Leaning in any direction will only increase the chances that you will slip out of the saddle or get thrown over the horse's shoulder. Grab onto the horse's mane or the front of the saddle (or saddle horn, if you have one) for extra stability during the rear. Assess your horse's current attitude. If your horse has just reared, there's a chance it may try to rear again. You'll need to assess how the horse is currently acting/reacting to determine if there's a chance the horse will rear again. If it was just a one-time rear and your horse has continued walking calmly, you should be safe. However, you should still be on guard in case it happens again. If your horse is balking and appears to be "threatening" to repeat another rear, you'll need to hold on and try to prevent it. Prevent a repeat rear. Now that you've pulled your horse out of a rear and assessed its attitude, you'll need to take precautions to prevent another rear. If you feel that your horse might repeat another rear, you may not be able to fully prevent it, but you can reduce the horse's ability to rear up. This will eventually calm the horse down until it is more stable and willing to ride or walk back to the stable. Tighten your grip on one of the reins (but not both). Pull that rein out to the side as far as you can go, and with as much strength as you can. This will lead the horse into a half-circle or a turn. Keep that rein off to the side until the horse is fully calmed down and no longer threatening to rear. If the horse attempts to rear again at this point, it will be significantly less powerful and less effective. The horse will be forced to move horizontally, and even if it tries to rear it won't put you in nearly as much danger. Determine the cause of the rear. Once your horse is calm and the situation has been defused, you'll need to figure out why your horse reared up in the first place. The first thing you should consider is whether something scared your horse on the trail or in the field. Look around your immediate area for anything your horse might have been frightened by. Remember that your horse may have been frightened by something other than an animal. If your horse has never crossed a creek before, for example, it could be frightened of the water. If there is nothing in your surroundings that could have caused the rear, your horse was most likely either uncomfortable (perhaps with the bit you've used, or the way you're riding). Assess what might be the problem. Once you've ruled out a fearful stimulus in the horse's immediate environment, you can safely assume that the horse is uncomfortable or otherwise displeased with the way you're riding it. It now falls on you to assess what the problem might be and take the necessary steps to correct/avoid that problem, which is most likely an issue with the equipment you're using or the way you're riding your horse. Check the horse's bit. A painful or uncomfortable bit is often the cause of what appears to be bad behavior. If a bit does not fit the horse's mouth well, the horse may be distracted or even in pain. If your horse's mouth is actively in pain when you ride, it's no surprise that the horse would react to the pain and try to free itself from the source. A horse's age, mouth size (height, width, and depth), tongue thickness, lip thickness, and head length can all affect the way a bit fits in a horse's mouth. Depending on the horse's temperament and level of discomfort, a poorly-fitted bit could potentially lead to continued rearing problems. Talk to a horse equipment expert at your stable or at an equine supply store. Take measurements of your horse's mouth and head size, bring some photographs showing the horse's lips and face, and consider trying a different bit. Evaluate your own riding style. If there is nothing wrong with the bit and you're certain that nothing in the field startled your horse, your riding style could be the problem. Check your overall form and think about whether anything you're doing could make your horse uncomfortable or send mixed messages about what you want the horse to do. Your horse could be uncomfortable and frustrated if you give it conflicting signals. For example, kicking your horse forward while simultaneously pulling back on the reins will confuse and irritate your horse. If you're poorly balanced in the saddle, your horse may also try to rear out of frustration/discomfort. Practice groundwork. Doing regular groundwork practice with your horse is the best way to control its feet. If you've been having problems with your horse rearing, groundwork should help reduce the risk of future rearing. Retrain the horse to stop by teaching it to step back in response to light taps with a long whip on the front of the horse's shins. Practice keeping your horse's head down to avoid future anxiety-induced rears. Apply downward pressure by standing next to your horse while it's "parked," holding the reins under the horse's chin and gently rocking your hand side to side, then releasing once the horse lowers its head. Practice these techniques while standing on the ground, and once your horse has relearned these skills you can practice them while in the saddle. Reward your horse with treats that it likes, and give your horse verbal praise. Give your horse plenty of exercise. Too much time indoors can lead to undesirable behavior in many horses. Even if you can't get your horse out on a trail, your horse will still find being in a paddock preferable to being in the stall. Spend as much time as you can with your horse, and make sure your horse gets as much exercise and outdoor time as possible. A lack of exercise may not be the direct reason why your horse balked and reared, but it could contribute towards a sense of mistrust or resentment of your command. Your horse should ideally get several hours each day of pasture time with other horses, or riding/exercise time with you or another rider. Get help from a professional trainer. If your horse is still exhibiting rearing problems, your horse may have learned that rearing will get it out of doing undesirable activities and following commands. If this is the case, your horse may need some retraining from a professional trainer. A professional trainer will be able to assess your horse's behavioral problems, work directly with your horse, and give you pointers on how to prevent problems like rearing in the future. You can find professional trainers by checking in your local phone book, or by searching online. Make sure your trainer is certified, and don't be afraid to ask about his or her experience and educational background. Be patient with your horse. Remember that your horse is not trying to be malicious, and with time and some hard work, you and your horse can become life-long partners. 
Loosen the reins. Stay in the center of the saddle. Assess your horse's current attitude. Prevent a repeat rear. Determine the cause of the rear. Assess what might be the problem. Check the horse's bit. Evaluate your own riding style. Practice groundwork. Give your horse plenty of exercise. Get help from a professional trainer. 