Let's look at each of these elements individually.
We all know how hard it is to shoot a good group, or even hit the target sometimes, if we are breathing while we are pulling the trigger. When you breathe in, the abdomen expands, which can push the arms up and off target. When you breathe out, the reverse happens. The way to compensate for this is to take a deep breath, release about half of it, and fire your shot. If you are not under any time constraints, you can do this between every shot. If time is a factor, you may have to fire multiple shots on the same breath. If you start to see stars, or your vision starts to go dim, you might want to let that breath out and get another.
The more you relax, the better you will shoot. I have seen people try to stiff-arm their weapons to eliminate recoil instead of going with the recoil and it just doesn't work. On the other hand, you don't want to go all limpy wristed with that new .44 mag you just got, unless you like the idea of a large knot in the middle of your forehead.
There is a happy medium. Grip the weapon (we are referring to handguns here) in a firm but not choke-the-life-out-of-it grip. Keep the elbows unlocked, with the strong side arm a little straighter than the off side arm. Push forward with the strong hand and pull back with the off hand to establish some isometric pressure. Place your index finger print on the trigger, and you are ready to go. Remember, the more you relax, the better you shoot.
Aim consists of sight picture and sight alignment. Sight alignment is placing the front sight in proper alignment with the rear sight. When looking down the sights of your handgun, you should see a square "U" shaped rear sight with the top of the front sight even with the top of the rear sight. There should be an equal amount of space to the left and right of the front sight in the "U" of the rear sight. Sight picture consists of maintaining proper sight alignment, and placing the top of the front sight on the target. You should be able to see the front sight clearly and the target should be a little fuzzy. You can switch your focus from the front sight to the target to make sure you are still lined up while taking up the slack and squeezing your trigger.
Most handguns have a certain amount of slack or slop in their triggers. You will need to slowly put pressure on the trigger until you feel this slack is gone. Then re-check that you are still on target and continue the squeeze. Different weapons have different amounts of slack, so find out what yours has and learn to take it up before firing.
When firing any weapon except a shotgun, you want to squeeze, not jerk the trigger. Jerking causes the sights to stray from the target, and causes you to miss. After you have taken the slack up and checked your sight alignment and sight picture, continue to gently squeeze the trigger. The exact moment the weapon fires should be a surprise to you. Make sure that you place only your fingerprint on the trigger, or your trigger pull will not be straight back, and will cause your shot to go to one side or the other.
Hopefully this will help make your firearms practice more accurate and therefore, more enjoyable. Remember, practice doesn't make perfect, Perfect practice makes perfect. Don't learn any bad habits and you won't have to unlearn them later
Remember...practice while you have time...you don't want to learn AFTER the SHTF.