And now for the disclaimer, which is that this is all personal advice from me to you, and that the limit of my liability is what you're paying for this advice -- which is zero dollars. Feel free to cross-check what you see here elsewhere on the internet.
If you are loading a car onto the back of a trailer, and using ramps, then put a couple of piles of wooden blocks under the rear end of the trailer, to keep the weight of the car from forcing the tongue upward. The trailer's coupler is not particularly designed to hold negative weight, and you want to avoid putting thousands of pounds of upward force on the coupler, and also on your car's bumper or wherever else the ball might be mounted.
If you load anything movable, especially a car, then make sure it is well secured. For cars and other similarly heavy loads, this is what chains and binders are usually used for. It is _so_ important that a vehicle, which wants to move by its very nature, be kept from moving back toward the rear of a trailer that it is advisable to apply several different methods of restraint to your vehicle. How about the emergency brake, putting the car in low gear or park, and putting a chain or two up front, with another in back, just to start with? Use more chains if practical; if you are driving down the road and your car slides or otherwise moves toward the rear of your trailer, this can incite sway and cause a most spectacular crash.
The same goes for anything else that's heavy enough to be a significant portion of your load. Let's say you have a large milling machine and it tips over toward the rear. Other than the damage to the trailer and the machine, if this change in weight to the rear causes the swaying speed of the trailer to go below the speed you're currently driving at, you may immediately start swaying and go out of control and crash. So keep in mind that, while we mainly think of tying the load down to keep it safe, on the trailer, and to keep it from damaging other items, this shift in weight toward the rear is the biggest consideration when hauling anything of any significant weight.
Otherwise, you're just left to deciding how to tie down your items. For larger loads such as cars, trucks, or machinery, chains and binders can't quite be beat, although large nylon straps with rachets are pretty good too. For medium loads, such as a good-sized motorcycle, furniture which might blow around at highway speeds, or the like, nylon straps with the locking buckles or rachets are pretty good. Rope is good, too, but it's nice if it has a certain amount of stretch, since it's amazing how often loads will work loose under the constant jostling of going down a highway on a trailer. At the smaller end, elastic/rubber bungee cords have the advantage of always keeping the load tight, even as it moves around a bit. Sometimes putting 10 small bungee cords on a load it more advisable than running a rope around it and hoping it won't loosen up.
For smaller trailers, I judge by whether I can pick up the tongue myself. If your load is very high at all, which means that the tongue weight will change dramatically depending on how high the tongue is, then block the tongue up at towing height before checking this of course.
For larger trailers, you may not be able to pick the tongue up at all by yourself, even when the trailer is empty. I still like to check these trailers by hand, and will often load small heavy objects at the rear of the trailer so that when I'm done loading, and can just barely pick up the front of the trailer, I can move these objects from the rear to the front. Moving a 40 pound concrete block from the rear of a trailer to the front, for example, will make about a 90 pound difference in the tongue weight. Moving a couple or few objects like this gives you the idea that you're in the ballpark for tongue weight.
There is also the old trick, which should come to you intuitively after a while, of counting the number of turns on the trailer's jack handle. From the time that the coupler settles onto the ball on your towing vehicle, you count until the jack's foot comes off of the ground. On my Explorer XLT, this is about 10 turns, and the car sinks about 1.5 inches. On my other vehicles, the amount of turns varies, of course, but this is another good way to get in the ballpark. You can also just use a ruler and check how much the vehicle sags as the tongue weight is applied.
It is important to get the weight on the tongue correct, since if you have too little weight on it, your trailer will be prone to swaying at higher speeds. I find that for most vehicle combinations, this effect won't happen below 50mph, but that is just a general guideline, and you must learn to identify the onset of swaying, and the other effects of misloading your trailers.
Keep your towing vehicle's mirrors adjusted so that you can see the rear corners of your trailer(s), since probably the best indicator that swaying is imminent is the continual movement of the rear of your trailer. You might be able to make a trip like this, but it's after not more than a few more miles per hour, maybe 5 in most cases, that swaying can become severe, and it's very easy to pick up 5-10mph on a downhill grade. It's much better to make sure that you are nowhere near swaying speed by raising the speed that swaying will occur at, and proper loading can raise this speed far beyond how fast you're likely to drive because of other factors, like speed limit, tire heating, and the ability to stop in a reasonable distance in case of a tire failure or the like.
Enough weight on the rear of the trailer can set up an oscillation which feeds upon itself. Hitting the brakes makes it worse, by the way, so your best hope is to simply stop accelerating, turn off the cruise control, or, if headed downhill, to apply the brakes enough to keep from going any faster and hope that the swaying doesn't get any worse.
Swaying will tend to plateau for a little while at the point at which the scrub of your trailer's tires, and to a certain extent, the towing vehicle's tires, aborbs some of the energy in the system and slows your combination down. However, if you're at the point where you're still picking up energy, such as going down a hill, or if you happen to go over a few badly timed bumps, you can surpass this point, at which time you will crash, all other things being equal.
I am not a mechanical engineer, and so if anyone has any more insightful observation on this subject, I will be happy to add them to this page.