First off, I'm not a qualified firearms instructor. I can relate only what has worked for me over the years. This is pretty old school stuff.
It's pretty obvious and basic isometric tension for the most part. You can use a blue gun, or an unloaded weapon, or bare hands for that matter, but it's probably better, initially, to use a prop. The trick is to go all out.. crush it. Take your normal shooting stance, or hold if you want to do this seated at a desk, and then intensify this position as strongly as you possibly can. Tighten the grip, the arms, shoulders, chest and hold that extreme tension -- and at the same time, use your trigger finger to gently tap out your count in seconds. While doing this, slowly rotate your head left and right as far as you can and still be able to see the sights (relaxed trigger finger AND neck muscles are key -- no tension in either area and that most likely will take some concentrated 'letting go into relaxation' of those muscles in the beginning). Begin with however long you can hold it, say, a tap out of 10, and work up from there. If done correctly, you'll feel it.. big time.. Begin with two or three reps of this and work up to five - three times or more a day.
The ability to fully control the weapon using a lower percentage of your strength capacity is what this accomplishes.
For the trigger exercise, one of the best things to use is an old, cheap revolver that has the usual, you know, 762lb shitty revolver trigger. The exercise is exactly opposite. You want to hold the weapon(?) as lightly as you can with your hands, and concentrate moving the trigger finger only. Slowly, ridiculously slowly, pull the trigger through the break. On every 5th or so pull, stop and hold the trigger mid to late pull for a count of 10, 15, 20, whatever, making sure your hands are remaining as relaxed as possible, then continue through break, lather, rinse, repeat for say 20 pulls (whatever you can can reasonably comfortably do) at the beginning and work up from there.
This one is working on trigger finger independence and strength simultaneously. You can also use one of those hand exercisers with independent finger springs, but the key is to, as much a possible, relax the other fingers while working the index, and conversely, gently tap the index while holding the other fingers in a one handed grip.
May seem silly, but these do work. Do this for a month and you should see a marked improvement at the range as well as a reduced fatigue level. I still do this stuff, perhaps not every day anymore, but several times a week like clockwork.
I'd be interested in hearing about other exercises, perhaps some new and improved ones by you newfangled shootin' gurus, or more old school tricks that have been proven over time. Chime in.