Congrats and hello. Nice to meet you. Welcome!
I found that the push/pull method worked for ME with handguns. Not a HARD push/pull but a light to firm grip. I shot better at my "perp paper targets" aka silhouette paper targets.
The other suggestions were very good here too.
Most of my 1998-2001 early shooting was up close and personal self defense shooting/learning. Indoor range and later on at an outdoor range - sportsman's club, back east. I still do that 'self defense' up close shooting. I shoot up to 50 yards for general plinking. I rarely shoot at the other longer range ranges although it is there for me if I want to use it out here.
The NRA has a great book on pistol shooting - steps, safety, etc. A class might help you too. Practice helps tons! Jeff Cooper, Mas Ayoob, Paxton Quigley, etc. have great books too.
Mas has articles on this magazine website too. You can buy the magazine too.
http://www.backwoodshome.com/
I shake more with a rifle of any kind than I do with a s/a or d/a revolver or semi automatic pistol due to a bad left arm.
I like to shoot standing UP. I do not like bench rest for hand guns or rifles. NO offense to ones who love it.
Weights - light weight ones and swimming laps will help the shakes if it is a strength problem, former old accident and/or arthritis. Your breathing, relaxed state, your stance, your concentration, focus, etc. all help.
If you don't feel that you need to be 'perfect' right away, ask questions and follow the instructions or tips on what you may or may not be doing wrong... that helps too. I felt the need to be 'perfect' but I am the type to ALWAYS ask questions, study and ask for tips on doing Anything (Grin.) - especially when I got into firearms more! So when my late husband and other men, who KNEW what they were talking about including ones who COMPETE, told me where I screwed UP and suggested other things to me - I paid attention! I REALLY wanted to learn it ALL from a to z! My groom/husband used to compete every week when he was on another office schedule here in Montana. He is a GREAT shot and hunter too. My late husband was not a hunter, shot some but was a GREAT self defense shooter. He had to 'qualify' for the military. NOT too much 'qualification' though as a USN destroyer man and an Air NG Fighter Wing man. He was NO sniper but did a good job. I think that he was a natural in some things as my groom is in 'shooting'. Some people are naturals in shooting and in various other subject matters.
RELAX, learn and practice tons. Pace yourself too. I had to pace myself using various calibers when I first learned and got into shooting more. I still pace myself now - left arm is worse. I found that if I go up to stand at the 'line' aim at a gong @ 50 yards... I can sometimes HIT it almost immediately and in fact - a few times with a single action revolver. When I get tired... my hands get weaker and I tend to shake more at that time. I do better - fresh and right off the bat/gitgo or after a 'break' too.
Take your fluids with you and drink water or Gatorade powder/water.
Coffee and tea don't bother me before shooting. No Rx meds here only aspirin and vitamins/minerals so no problem there for me.
Some Rx meds might bother you - only you will know that.
Have something in your stomach so you don't shoot too full or too hungry. That helps me too.
Former indoor range back east when I first learned:
My first time when not using my Glock Model 19C - I used to shoot TOO HIGH! When I first learned other guns - ALL calibers other than that older 357Magnum of his - I made head and neck shots. I was not aiming for that but I made them often. He told me - center of mass, etc. Lower... so I did that and hit the perp target in the groin. Finally I figured it ALL out!
I am not an EXPERT shot, I am NO expert in firearms nor a WAY FAR away shooter like some gals/guys. I can defend myself in a 'situation' - up close and personal. I can plink up to 50 yards too. I can hit some targets 'sometimes' farther than 150 feet but I think that is just LUCK or if I used his rifle with a scope. Way far away shooting does NOT interest me. NO offense. I go on hunts with him but I don't officially 'hunt'.
Men told me that I was easier to TEACH. My late husband, military, police, gun buddies and my groom/husband. They said that I did not come in with bad habits or 'an almighty attitude' on knowing it all. I was a newbie and ignorant but I wanted to LEARN and wanted to be able to defend myself if needed. I ALWAYS admitted to being a newbie back then. I did not learn more than the basics and get into 'shooting more' until I was almost 48 years old - 1998. I am not a newbie or novice but I have only been shooting on a regular basis for 10 years now.
Best wishes.
Catherine