This is the strike that you do first in every single lesson. Although it's name is generally translated as "stomach-level punch", the term "chudan" actually means mid-level. It's a good all-round strike, and depending upon the force that you use it can offer multiple levels of damage. Performed with moderate power to an opponent's stomach, it can wind someone sufficiently for you to escape a hostile situation, without causing serious harm. In life-threatening situations, a punch to the sternum (breast bone) can crack it or even stop someones heart. Like all karate techniques, it should be used with caution and only as a last resort.
For now, just stick your left fist out in front of you with your palm facing downwards, as if you've just punched someone in the stomach.
Retract your right fist so that it's positioned by your right side just level with the bottom of your ribs. Your palm should be facing upwards. It's very easy to let the elbow of your retracted hand stick out as if your impersonating a chicken, and to correct this, many instructors will tell you to pull your elbow right in, which is equally incorrect. Given that you will be punching to the centre of your body, your elbow should stick out at a reverse-angle equivalent to the angle your arm must extend forward for your fist to hit a mid-point in front of you. Why? Because if your elbow is retracted exactly perpindicular to the direction you're facing, your punch will follow an arcing path to its target, which is slower and less powerful.
Now moving your right fist in a straight line, punch in front of you at stomachor chest height. Your right hand should remain palm up until the very last moment, when it rotates 180 degrees to finish palm down. Be careful to maintain the correct alignment of bones in the hand. The last moment rotation serves two functions: first, it adds to the overall speed and power of the punch, by adding rotational velocity to the linear velocity produced by throwing your fist forwards. Secondly, because the rotation occurs at the moment of impact, it can increase the damage caused by the punch. If you hit your opponent in a boney area, such as their cheek, the rotation can split the skin, whereas if you hit them in an area of soft tissue, it can disrupt the underlying muscle or organs. That's not something you'd want in a dojo of course, but if you're fighting off a mugger or a rapist, you might be glad for a little bit of blood that can run into their eye!
The final position for the right arm should be almost fully extended, with the fist striking mid-level. I say 'almost fully extended' because like most techniques in GKR, you don't fully lock out your arm. I expect you're thinking "But why not? Surely it would be better to lock the arm out?" Maybe you can get a few extra centimetres by fully locking the arm out, and maybe it does make it harder for your opponent to rush in and collapse your arm against you. In a real fight, it makes sense to lock your arm out. The trouble is, in a dojo, where you'll be repeating the same action thousands of times, you can permanently injure yourself by doing so. Oriental martial artists tend to be shorter and slighter than their counterparts in the ret of the world, which means that the stresses placed upon their joints by repetitiously locking their arms out is far less. Studies have revealed that locking your arms out fully during a punch can lead to arthritis and rheumatism in later life, especially for taller karateka. If you need any further convincing, remember that karate is about control. It demonstrates no control to simply throw a fist out to the limit of its movement before stopping, but it takes far greater skill to stop short. You could have punched further, but you chose not to...
Anyway, as the right arm extends forwards, the left arm is retracted backwards, also doing a 180 degree rotation at the last moment, as it comes to rest beside your left side. This rotation is merely done in preparation for a subsequent punch.
The key to a good punch is relaxation. You need to keep every part of your arm from shoulder to hand, as loose as possible through the initiation (start), and delivery (travel) phases of the movement. It's only as you strike that you clench your fist and tense your arm muscles. Some instructors suggest that one way to ensure suitable relaxation, is to concentrate on the other arm rather than the one that's about to strike, trying to retract it as quickly as possible. I have mixed feelings about this approach, but try it and see if it works for you.