The instinctive thing to do is to grip the bow firmly. However, doing that, or worse, grabbing the bow suddenly as you execute the shot, will force the bow to twist. You might think the arrow is gone by the time you grab the bow, but it does affect the shot. You will never do it exactly the same each time, so it results in wider groups.
To start with, you really must have a sling (unless you shoot a longbow). This will catch the bow and stop it falling on the floor. Choose a style that you like, and adjust it so that it is slightly loose. The bow needs room to move forwards and leave your hand for a moment as the arrow leaves the string. If you shoot a longbow, you can still use a relaxed hand, just touch your first finger and thumb together to act as a sling and let the bow leave your hand. This will only work if your arrows are correctly spined, though, otherwise the bow will kick too much in your hand.
When you pull the string slightly in the pre-draw, this is the time to get your bow hand right, before you lift the bow to the target. Your hand should be placed on the bow with your knuckles at about 45 degrees. Allow your wrist to bend downwards slightly so that you feel the bow being pushed against the muscle at the base of your thumb. A lot of people seem to be trying high wrist positions at the moment, but a high wrist is actually less stable than a low one. The point of contact should be aligned directly down your forearm, i.e. your wrist must not be bent sideways. Most important, your fingers must be be fully relaxed. You then need to keep this relaxed position as you lift the bow, draw and execute the shot. The bow is allowed to move. A properly set-up bow will move forwards as the arrow leaves the string. You need to let it do that and trust it to do what it wants to do.
Having trouble? If you find yourself grabbing the bow, try holding a cork gently between the tips of your thumb and first finger. If the cork is tied to the bow with a piece of string it makes it easier. When you let go, the bow should knock the cork out (which is why you tie it to the bow so it doesn’t fly off down the range). The biggest hurdle for most is having the confidence to let the bow leave your hand and trusting that the sling will catch the bow. Shoot at a short target with no face so you have no distractions. It can be a bit of a leap of faith, but trust the sling. Take your time and shoot lots of arrows at the short target to get used to how it feels.
Does the bow kick sideways? That is a sign that something is wrong with the set-up, so fix that first. It could be your arrows are the wrong spine, or your pressure button/launcher is in the wrong place.
Some people will deliberately hold their fingers out straight. This is better than grabbing the bow, but isn’t great as you are still putting tension in the muscles in your forearm which work your fingers, and tension inevitably means unwanted movement, not to mention a waste of effort. Relax those fingers, even if you have to spend time just drawing the bow without shooting to get used to how it feels.
The shape of the grip is important to all this as well, although ‘grip’ is a slightly unfortunate term. The ideal shape for most people is a flat surface angled slightly away from your fingers so it matches the shape of your hand. See the Hoyt Ortho or Jager grips for examples, or make your own. Grips on newer recurves are generally better than they used to be, but don’t be afraid to modify a grip with tape, body filler or whatever to get it the right shape. If it all goes goes wrong, file it down and try again, or just start with a new one. OK, you might not want to do that if you have splashed out on a Jager :-), but most grips are quite cheap. Grips on compounds tend to be very narrow, but bear in mind the vast majority of compounds are designed for the US hunting market rather than for competition target shooting. Target archers need a grip that is comfortable and consistent over a lot more arrows. Some say that a narrow grip minimises torque, but if your hand is in the right place and relaxed you won’t be torquing it anyway.