How can I hold a chefs knife for efficiency and safety?

There are a couple ways I hold a knife.

One, my go-to grip, is a thumbs-up grip - with my thumb braced against the back of the knife blade, and my fingers wrapped around the hilt. Usually, I'm using my other hand curved over the blade, to move the food on either side, or add additional pressure to the knife as it cuts. I am using the blade like an extension of my thumb, pressing down with weight behind it - and it is really good for rocking cuts.

Another grip is with my forefinger along the length of the blade - this gives a bit more precision in placing the knife, but less force behind it. This would work for making long rocking cuts, where I need the length of the blade (it extends line of control further), or for slicing, and also for making delicate cuts, or teasing things apart with the tip of the knife. This grip it really helps to use the other hand to give extra pressure along the back of the knife blade.

And the third, is very nearly a pinch grip - except moved back about an inch, so my grip is wrapped around the handle, not the blade. I am pinching the handle, just behind the blade, between my thumb and the side of my forefinger, with that finger curled along the side and slanting under the handle, and my other fingers wrapped loosely around the hilt. It's possible to edge the grip forward just a bit, so that the side of the forefinger edges into the gap where the blade falls away from the handle - but the finger is still far enough back that it can wrap under and behind the blade, and the thumb is still on the handle. This can make a very secure grip.

The pinch grip is kind terrible, I agree with @Joe, it pulls the knife out of balance and makes the grip weak. The difference between the width of the blade and the width of the handle weakens the grip, since the pressure has to be variable, and the majority of the index finger is kinda hanging out into space, not involved in the grip at all. The whole thing is kinda awkward, and the videos show the thumb pointed across the blade, while to control the cut it needs to be nearly horizontal along the blade, which pulls the forefinger out of alignment unless you pinch against the side of the finger, not the pad - in which case it's more comfortable and controllable to move the grip back along the hilt to the handle.

This is somewhat dependent on the exact knife you use. Generally, all grip styles have their use for different cuts and ingredient. The balance of the knife has a lot of bearing on the exact grip that is safe and comfortable with it - a blade-heavy one (typical of asian style) will handle differently than a handle-heavy one (typical european style).

Look at video material of professional and experienced amateur chefs - you can get a visual impression of how efficient and/or accurate their style is, and you can usually assume these people have learned safety by instinct or mistake.

My favourite way of holding knives with larger blades would be to use the pinch method. Personally, it feels the safest way to hold the knife and it also give you superior control of where the blade will go. That being said it wont flop sideways on you and it's less likely to make your slices less straight.

Simply hold the knife handle with your pinky ring and middle fingers wrapped up under the bottom of the handle and touch them to your palm with a firm grip on the handle aswell. After, use you index and thumb to pinch the top side of the blade closest to the handle.

This method automatically gives you a sense that you have more control over the knife and offers more force into the cuts especially with harder vegetables like butternut squash.

The only draw back of this method is if your new to it then you will most likely get a blister on your index finger which isn't always pleasant. Surely, after a while of using this method you will develop what they call your chef's callus and it wont be much of an annoying problem after that..

With a regular chefs knife, I'd recommend "the pinch" as suggested by Joe. Youtube explanation

However, some chefs knives don't have a wide enough blade. This means that you will have difficulty holding on to the knife and your knuckles will hit the cutting board.

Another frequent problem with chefs knives are the sharp edges on the spine of the knife. If the spine hurts your hand (you can even get blisters), you can round these corners with sandpaper or a file.

Anthony Bourdain recommends Vanadium steel for cooking knives. These are inexpensive and can be easily sharpened.