The first thing is to forget about the whole "problem" of single-beveled knives. A yanagi, or in fact any knife for cutting sashimi (e.g. a takobiki, fugubiki, etc.), is so thin-bladed that any tendency of the knife to turn in the cut is trivial.
As to cutting technique, there are of course many classic cuts for sashimi, but the two you're most likely to use are as follows:
1. With thick, square blocks of fish that have minimal "grain," e.g. tuna, you normally cut with the blade straight up-and-down, making rectangular planks of a thickness appropriate to the cut and type of fish.
2. With a full or half fillet of a smaller fish, laid flat on the board skin-side down (whether it's got the skin on or not is another matter), you normally turn the blade so the spine is away from you and the beveled side is at about a 45-degree angle (precise angle depends on the fish grain) to the board.
In either case, you will be cutting with the flat side of the blade (actually very, very slightly concave) toward you and the beveled side away. The fingers of your off-hand will guide the blade on the flat side, never the bevel. With the knife used this way, the bevel will never work against you -- that will only happen if the knife is extremely thick (which a sashimi knife isn't), the object being cut is extremely deep (which fish prepared for sashimi cutting isn't), or you turn the knife over (which is almost never done with sashimi knives).
This takes us to two important issues: length and sharpness.
How long the knife needs to be depends on how heavy it is and how sharp. How heavy it is depends on how it's made and how it's sharpened. How sharp it is depends exclusively on how sharp you keep it: nobody will sell you a sashimi knife that is sharp enough, unless you are in a knife shop in Japan and beg very, very nicely -- and pay a lot for the service. So the most important consideration is sharpening.
Think of it this way. When you cut sashimi, you normally use a draw-stroke, which means that you pull rather than push the knife. Ideally, you cut the fish in a single pull. Consider the straight cut, for blocks of tuna. Put the knife, just a hair forward of the heel, on the far edge of the tuna block so that the point is just very slightly down but not touching the board. Push forward a tiny hair -- forward, not down, letting the weight of the knife at the heel start the cut. Now start drawing the knife back in a smooth, even motion. The handle should arc downward as you do this, then go straight back. The point should thus swing upward, back, and down in an even curve. By the time you are halfway through the pull, so the middle of the knife is in the tuna, you should be pulling essentially straight backward, and the tuna should be about 1/3 cut, give or take. The remainder of the cut, pulling straight back and letting the knife simply fall, uses the fact that the majority of the blade weight is near the tip, where the knife is also thinnest, and the rest of the slice is cut with just the last generous third of the knife. Ideally, the cut finishes with the tip just barely grazing the board as it exits the block of tuna.
Now in order to do this, you need a heck of a lot of practice. But you also need a knife that is very thin, rather heavy, and extremely sharp. But thin and heavy don't go together: the thinner the knife, the less it weighs, assuming it's made of steel and not depleted uranium or something. So you get the weight primarily through length. This is why sashimi knives are so long --- and 270mm is hardly long here: 360mm is long.
The other classic cut, which I won't describe in such detail, begins much the same, but the knife bevel is laid against the surface of the fish fillet at the appropriate angle. As you draw, you gently hold the fish slice in place with the flat fingers of your off-hand, fingertips pointing toward the blade spine, fingers themselves as close to parallel to the blade flat as is possible. You generally need a little more force to get this cut started, but lower in the fillet any force from your hands will tend to tear the slice, even a little bit, so everything has to come from that scary-sharp pointmost-third of the knife.
My feeling is that you need to think very, very seriously about just how often you're going to cut sashimi:
A. Fish of sufficient quality is expensive in the U.S., and with very limited exceptions is always pre-frozen, which doesn't do anything too great for the texture. I don't know, though, you might not live in America, or you might do your own deep-sea fishing, or whatever.
B. A sashimi knife is an investment, and from your post it doesn't sound as though you currently have a whole lot of expertise with it. This means that if you intend to get serious about this, you have to plan ultimately to buy several more such knives. What I mean is, you don't want to buy the best sashimi knife in the world (rather debatable what that would be, but...), for the same reason as you don't want to learn how to drive with a Ferrari. But a sashimi knife of enough quality that you can learn well is not cheap.
C. Maintenance of a sashimi knife is a very serious business. It must be kept frighteningly sharp, especially near the tip, or it won't work right and you will be frustrated -- and learn bad habits. If you're serious about this, I would recommend that you consider something like an Apex EdgePro or similar high-end manual sharpening system, unless you are an extremely practiced freehand sharpener: a single-beveled knife is easier to sharpen, in some respects, but the thinness and flexibility of a sashimi knife, as well as its length, makes freehanding quite a bit more difficult.
D. I don't speak from personal experience on this one, but some people whose opinion I greatly respect say that a takobiki or fugubiki is a great deal easier to learn than a yanagiba. What's more, the skills are sufficiently the same that once you have really mastered one of the "easier" knives, you can graduate to the yanagiba without having to completely retrain yourself.
E. If you just want to try it out, see whether this is something you want to get more seriously into, I think the very first thing to do is to find someone -- quite possibly through a woodworking shop -- who is really expert at sharpening single-beveled knives and knows a lot about them. Talk to this person, and try to get a feel: can he or she really bevel the knife appropriately and put that terrifying razor edge on it? Does he or she know clearly what is involved? Has he or she done it -- often? What sort of equipment is being used, and why? If you find such a person -- you can, if you look -- buy yourself a decent-quality stainless or semi-stainless takobiki or fugubiki through one of the Japanese knife-retailers with a good rep (Boar_d_laze, who will chime in soon, can give you a list of such places). Buy 270mm. Expect to spend some cash here, but you shouldn't have to put the kids in a workhouse. GET A SAYA, i.e. a wooden sheath, that fits the knife. Take your knife to the sharpener and get the edge properly beveled and sharpened -- Japanese knives rarely come fully finished. Now you're all set, and can start working with your fish.
Warning: never, never, never let the blade touch anything but boneless fish flesh. It should touch the cutting-board as little as possible, and when it does touch it should be in motion, under its own weight alone, moving straight, and you should be lifting it up ASAP. The blade will chip faster than you would believe. There are ways to use these knives when bones are involved, but don't go there until you are quite confident and knowledgeable.
Warning: when you put the knife into or take it out from the sheath, hold it spine-down by the sheath. Pull the knife out so that the spine drags along the bottom of the sheath, and put it in precisely the same way. Otherwise the sheath will dull and possibly chip the knife (though the latter is unlikely).
Warning: if you are a lefty, expect to spend more than your righty friends. Sad but true.
If you find you just love this sort of thing, take some classes. See if the chef at a local sushi place will give you some lessons on his off-days.
Final warning: if you like this, you've just entered upon a dangerously expensive hobby, and will begin slowly accumulating a large collection of knives and sharpening equipment.
Oh, and by the way: if you just want to cut some fish every now and then, just buy a thin-bladed slicer and have some nut from the woodworking shop sharpen it like a razor. You can't use a sashimi knife for anything else. Nothing. And it's expensive.