To the OP, how old are you? As we age, we develop tremors. It's natural, it's unavoidable, and it's incurable. Well, there is a cure which I'll explain shortly but I don't recommend it in combination with shooting.
As others have pointed out, we all tremble a little. It's impossible for nearly everyone to hold his/her hands rock steady. It just won't happen. Furthermore, if you're an old dude like me (I'll be 64 in a month) then you'll know that the tremors get worse as you age. I'm at the point where, sometimes, holding a spoon or a fork steady in my dominant right hand becomes an impossibility. For me, eating something like soup in the company of others has become a bit embarrasing.
Still, I remain a pretty accurate shooter at distances of up to 25 yards. I've learned to compensate for my tremor by timing my shots to coincide with periods of relative quiet. My tremors are never the same from moment to moment, I'll have stretches of 10 seconds where I shake like a leaf and of 10 seconds where I'm as steady as if I've been carved from marble.
Here's a "cure" as told to me by my doctor. Drink a couple of glasses of wine. You'll be amazed that your hand shake will have disappeared. I don't know why it happens but it does. For obvious reasons, however, one can't do that before or even during a trip to the range.
