I shoot USPSA competition,, and I have discussed this very thing with several of the worlds best action pistol shooters.
Generally, They all figure out a practice routine that will help them with their next major competition. (If it's a USPSA match,, set up some drills to help that,, or a steel challenge,, they set those up etc.)
However,, quite often,, a couple of things have been said by most of them to help you become a better,, and faster shooter.
First,, daily,, in home,, dry fire practice. To include the draw,, and action work,, WITHOUT LIVE AMMO AROUND AT ALL!!!!
Next,, they warm up with simple drills such as having the buzzer go off,,draw & fire one round,, or double tap a target in a set of 30-50 reps just to warm up. They ALL have said that constant practice of the BASICS is one of the best things you can do.
Work on stance,, draw, proper grip, sight aquisition, trigger control, and follow through. Repeat often.