Have the heels of your hands touching each other. Don't press, don't cramp, but keep them together. Your hands will still be shaky, but they'll shake together.
Also don't start with too many different colours. Get comfortable first, then build on that. I am not good with fine motor skills generally and I am all but patient (ADHD, yay) but painting miniatures can be quite meditative. It took me a while though, and it is important to get the basics straight. A good rule of thumb is three colours plus details, primary (paint most of the armour with this colour, the big plates like legs, torso and backpack), secondary or contrast (paint some minor areas that you want to pop out like helmet or pauldrons with this colour) and tertiary or trim (paint small areas that separate armour parts or decals (like aquilas on vanilla marines' chests) with this colour).
Work on solid base coats and not painting over lines before you go crazy on your pallette.
This is just advice from my own personal experience though and if this is not working for you, that's fine, too. Most important is to do it in ways you are having fun doing.
Get a handle with a stabilizer bar. I have tremors in my dominant hand, but resting the brush against the stabilizer helps curtail their effect.