The first thing to know about renting a horse is that it is not like renting a car. The brakes and steering are not guaranteed to work consistently, if at all. If you want to safely learn to ride a horse, go to your local equestrian supply ("tack") shop and ask for recommendations on a good instructor. I am assuming that if you are reading this, you are not trying to learn anything and simply want to yahoo down the beach or the trail. Okay, let's try to talk about how to do that in a morally responsible manner - assuming you, like most people, believe yourself to be kind to animals.
First of all, trail string horses work hard for a living. Like anyone doing hard physical work, they need to get adequate nutrition in order to do their job. The horse pictured here is starving. See the bones on the side of his butt and how they stick out? That is not normal. Neither is seeing all of the ribs clearly outlined, or a spine sticking up from the back. Now, a healthy horse can have a shoulder that sticks up further (the part right under the front of the saddle) and that can be normal - but the back and butt should be round and filled in. This dude thinks he is having fun, but he has unwittingly been made a party to horse abuse. He looks like a nice guy. I am sure it was not deliberate - simply lack of knowledge. Don't be him. Now let's move on to feet. Feet should look neatly trimmed. The edges should not be all broken off and ragged looking. If they look like the feet shown here, do not ride. Tell them that the horse's hooves aren't in good enough condition to be ridden and you will not give them your business. When you do ride, if the horse is tripping frequently or taking short little steps and seeming to have trouble, he is hurting. Get off. Please refuse to ride a horse in this condition. It is up to you to take a stand. (And better yet, take pictures and report the establishment. That's why you have a camera phone. It is not just for sending pictures of your butt to your friends when you are shitfaced drunk!)
If you have dogs or cats, you're probably familiar with some of the other signs of illness in an animal. Yellow discharge from the eyes or nose, for example, is a sign of a problem. Coughing or heaving when trying to breathe is hard to miss and something that even a novice should pick up on. When you see these things - do not ride.
Look around the premises. Horses that are not being ridden should have free access to drinking water at all times, particularly in the heat. If you know how to check for dehydration in your small pet animal, the same goes with a horse - pinch the neck skin. It should snap back in no more than 1 second or so. More than that, and the horse probably is in desperate need of a drink.
OK let's say we're good up to this point and you decide to ride. Once they get you mounted and your stirrups adjusted, put your hand under the front of the saddle. Can you fit 2-3 of your fingers under the front of the saddle, between it and the horse?
If you can't, the saddle does not fit and the horse will be in great pain as you ride. That may cause him to act up or even throw you, so your safety is also an issue here! Complain and ask that a better fitting saddle be found. If they refuse, do not ride. The picture shows the area you need to stick your fingers into.
The bridle is also an issue. It is not normal for a horse to throw his head around as he is ridden unless you have a death grip on his mouth (more on that later). If that is happening, something is not right. Complain.
All right, we've gotten that far. If you don't know how to ride, how do you survive a trail/vacation riding experience? Here are a few tips you MUST remember:
1. Those reins are attached to a steel piece stuck between the horse's teeth. Imagine how that feels. You don't want to pull hard on it. If the horse is throwing his head, you are probably being too stiff with your hands. Your elbow is a hinge - use it that way. Give and take and try to "follow" the horse's head. You can pull and release, gently, to slow speed. Keep your hands low - if they are low (around the front of the saddle) they will be more effective. High hands just make the horse angry and irritated.
2. If the horse runs away with you or gets faster than you are comfortable with, LEAN BACK and make SURE you are not hanging on with your lower leg. Your lower legs are your accelerator, and when you hang on with them, you are STOMPING on the accelerator, making things worse! Even if you pull on the reins, gripping with your lower leg will override that. So LEAN BACK, get your feet out of the horse's side, shove your heels DOWN (this will keep you from losing a stirrup) and then, if you have space to do so, pull on only one rein and make the horse circle. This will slow his speed safely. Make sure you are ready to circle and lean into the turn a bit so you don't dump yourself off via centrifugal force :-) If you are on a narrow trail and the horse has gotten out in front, just lean back and pull-release, pull-release and say HO in as deep and non-shaky a voice as possible given the circumstances. Most horses do not want to leave the other horses, and while they may have a short burst of speed, trail string horses are simply not going to run for 50 miles. If they are heading for the barn and blasting full out, you NEED to circle. One rein and ONLY one rein will accomplish this. Just wind them right around and they will have to slow down. A horse who is bolting for the barn WILL run under things you don't fit under and through gates only big enough for him and not your legs. Circling will save your ass.
3. If the horse feels lame to you and/or is bobbing his head with every step, ask about it. If you are a beginner and can tell that the horse is favoring a leg, guess what, he's hurting pretty bad. When you've been riding for 30 years, you may pick up on very minor pain because it just doesn't feel exactly right to you. At your stage of the game, shoot, if YOU can feel a limp, that poor horse is in major pain. Complain. Ask for another horse and if you see them put the horse out in the string with a different rider, throw a fit. One exception to this rule is gaited horses - horses that do not trot. These horses may bob their heads as part of their normal gait but the gait itself will feel even and not like they are "ouchy" on a particular leg. If you aren't sure, better to be safe than sorry. Again, this is also for your safety. A lame horse is prone to tripping and falling and that can mean a bad accident for you. You want to have fun - not wind up in the ER in some third world tourist trap.
4. Sure, you are going to bounce at the trot. It hurts your butt and the horse ain't too fond of it either. You feel like a sack of potatoes banging on their kidneys when you bounce. If you have a rough gaited horse, try standing slightly in your stirrups at the trot. You can hang onto the horn, or the mane. It does not hurt a horse when you pull on their mane, not at all. This tactic will save your butt and the horse's back!
5. Dress appropriately to ride. Loose pants will mean a painful rub or blister. You have no idea how painful. Shorts - are you nuts? The best pants to ride in are jeans that are snug through the thigh and knee. You want to be wearing completely closed shoes that have at least a small heel on them. That will keep your foot from getting stuck in the stirrup - it's a big safety issue. A boot like the one shown here is really the best choice. These kind of boots are $20 at Wal-Mart - just go grab a pair before you head out! And of course, most western boots are just fine, if you want to look like a cowboy. :-)
Again, I am not recommending that ANY of you do this. I don't think trail string riding is safe and can tell you horror stories all day. But if you are going to do it, at least educate yourself and try to do it in a non-abusive way that does not end with you bringing a couple broken ribs and a crutch home from what was supposed to be a fun vacation!
(Comments on other tips and tricks and things to look for and avoid are VERY welcome!) Remember, we as the humans have the choice - and we choose with our wallets! Make a humane choice that is safe for yourself and your family.