It is interesting to notice that instinctually, people make fists differently. The proper fist is very important if you’re trying to punch someone. Not only is it critical in assuring you don’t injure yourself, holding your hand correctly can also affect the power you deliver.

To begin with, an easy way to make a proper fist is to hold your hand out, palm-side up. Curl your fingers inward as if you were holding a roll of coins. Then lay your thumb across the fingers as if to brace them inward. You should form a flat surface with the knuckles of your hand.

Never make a fist with your thumb inside your other fingers. When you punch this way you will end up breaking your thumb.

Never leave your thumb at the side sticking straight up or sticking behind the flat surface of your fingers. If you have nails, this might seem like an effective way to gouge someone’s eyes out. But if you hit the wrong spot, something hard and impenetrable by your thumb, you will end up dislocating your thumb.

Maintain relaxed in your hands, only tensing it up as you strike your target. Tensing your hand the whole way through a punch is a waste of energy and can actually result in delivering less power at the end. The only time you will want to hold tension throughout your punch is if you’re trying to do tension exercises. And even then, you will want to learn how to relax as you inhale and only tense when you exhale.

There are several ways you can strike a target with your fist. Most refer to it in reference to your knuckles. You either use the top two knuckles or the bottom three to execute your punch. The top two knuckles are normally used for a forward driving or downward strike. The bottom three can used in roundhouse punches and punching with your fist perpendicular to the ground. A slight adjustment at the wrist can change which knuckles you will strike with. It is important to understand which hand structure you will use to generate the most power possible.

When you punch, you should be generating power not just from the movement of your arm, but your whole body. It’s much like the instructions given to golfers and baseball players: the pivoting of your body is what generates the power for your strike. Unlike these other two examples, though, you must maintain a stable root or you will find yourself off-balance and vulnerable to attacks. You’ll also want to make sure you don’t “wind-up” like these other sports as you will telegraph to your opponent a strike is coming.

When you’re punching with one hand, you should always consider having your other hand ready or at guard. Never let is simply hang to the side as you may miss a critical attack or block that could end the match.

Of course, as you progress as a student, you will learn a famous saying that my Grandmaster repeats all the time:
A student hits with a fist
A teacher with an open hand
A master with a single finger
I would rather get hit with a fist than with someone who truly knows how to use their open hand to attack.