when I first started shooting, my hands didn't shake per se, not like Capt. Miller from saving private ryan, but the gun wasn't still and the sights would wander.
for me, it was a combination of stance, breathing, lower and upper body all moving and doing stuff.
you need to find the best grip (how you hold the gun) and stance that works for you. ask and look at how people hold guns(also look at their groupings and see how well they shoot before imitating them). some grips and stances are better than others, and some grips and stances will work better for you than others.
Me personally, I hold the gun in my right hand, and I mate my left palm to the 2nd knuckles of my right hand. so my left hand is significantly forward of my right. compared to the pancake grip where the 2 palms of each hand are opposite each other.
and I use modified weaver stance, where my feet are perpendicular to each other
*SAFETY FIRST*
and dry fire practice really helps out. get in your stance(don't practice dry firing sitting down), and hold your gun in your chosen grip, and then aim at something. focus on the front sight. is the front sight steady? shakey? wanders? its ok for your front sight to wander to a certain degree(very minimally), but it should be slow and steady. when your sight is on the target, dry fire the gun by slowly squeezing the trigger. do not snatch at the trigger when the front sight wanders over your target. did the front sight move? if it did thats not good. after you dry fire, are you still aiming at your target? you should be.
practicing this a lot will help you develop good shooting techniques. just sending lead down range without purpose will not
Also, how far away from you you hold you gun affects movement. A lot of people are inherently afraid of being near the gun, and hold it as far away from their face and body as possible. you can see then because they have locked their arms straight, and they are leaning away from the gun.
in my stance, both my elbows are bent and I lean forwardmy face not being more than 2 feet away (more like 18") from the gun. if you hold even a pencil at locked arms length your arms will move.
also, if you hold your gun at arms length, and take too long to aim, your motion and shaking will magnify, but in no way am i endorsing quick unaimed fire. you just need practice. the more practice you have, the faster things get through repetition.