The following is an explanation of the Rogers technique from M4Carbine.net member HeadHunter, an instructor at the Rogers shooting school.

At the Rogers School, we teach the students to straddle the magazine catch with the middle finger and thumb of the right hand.
We call this "making a tunnel" for the light.

The light is then pressed against the groove between the two digits rather than against the weapon itself.
This picture does not show the grip on the light itself, just the positioning of the light against the firing hand.

Seen from a front angle.

The flashlight is gripped between the forefinger and the middle finger with the switch at the base of the thumb.
Each person needs to find their individual grip so they can repeatedly index the light the same way.

The gripped flashlight is then placed against the tunnel formed by the thumb and middle finger of the other hand.
Note that the flashlight does NOT touch the weapon.
This accomplishes two things:
a) protects the magazine catch from the light, and
b) helps index the light repeatedly in the same spot.

The object is that the flashlight should be coaxially aligned with the bore of the weapon in both axes.
The vertical axis.

And the horizontal axis.

Note that if the flashlight isn't coaxial to the bore, the light will shine below the weapon's sights, typically at ranges in excess of 10 yards.
Night shooting is difficult enough without having the light and weapon pointing in different directions.

I have a high tech solution to help me repeatedly index the light the same way - a 1 inch O ring with a rubber band to keep it from sliding rearward.
Unsophisticated but it works better than anything else I have tried.
Strengths
The Rogers technique is, in my opinion, the absolute best technique when it comes to shooting accurately with a hand-held light.
The technique allows the three free fingers of your weak hand to grab on to the weapon and help to stabilize it. Once mastered, it allows you to shoot every bit as good as you can with a normal two handed hold.
Once mastered, it also allows you to put the hot spot of the light where it is centered around the front sight of the weapon the first time every time.
Weaknesses
The Rogers technique is probably the most difficult hand-held light technique to master. When you first try it out it is probably the most awkward and unnatural feeling technique you will try.
On some weapons the Rogers technique can interfere with the function of the weapon. It's particularly bad about ejecting magazines on some semi-autos.
While you can use the Rogers technique with many flashlights, it really does work best with lights dedicated to the technique like the 6Z/Z2 combat lights discussed earlier.
People usually require A LOT of practice to get the light indexed with the sights using this technique. Generally they end up pointing the light at the ground or way up in the air while the sights are more or less on target until they've mastered the technique.

At the Rogers School, we teach the students to straddle the magazine catch with the middle finger and thumb of the right hand.
We call this "making a tunnel" for the light.

The light is then pressed against the groove between the two digits rather than against the weapon itself.
This picture does not show the grip on the light itself, just the positioning of the light against the firing hand.

Seen from a front angle.

The flashlight is gripped between the forefinger and the middle finger with the switch at the base of the thumb.
Each person needs to find their individual grip so they can repeatedly index the light the same way.

The gripped flashlight is then placed against the tunnel formed by the thumb and middle finger of the other hand.
Note that the flashlight does NOT touch the weapon.
This accomplishes two things:
a) protects the magazine catch from the light, and
b) helps index the light repeatedly in the same spot.

The object is that the flashlight should be coaxially aligned with the bore of the weapon in both axes.
The vertical axis.

And the horizontal axis.


Note that if the flashlight isn't coaxial to the bore, the light will shine below the weapon's sights, typically at ranges in excess of 10 yards.
Night shooting is difficult enough without having the light and weapon pointing in different directions.

I have a high tech solution to help me repeatedly index the light the same way - a 1 inch O ring with a rubber band to keep it from sliding rearward.
Unsophisticated but it works better than anything else I have tried.
Strengths
The Rogers technique is, in my opinion, the absolute best technique when it comes to shooting accurately with a hand-held light.
The technique allows the three free fingers of your weak hand to grab on to the weapon and help to stabilize it. Once mastered, it allows you to shoot every bit as good as you can with a normal two handed hold.
Once mastered, it also allows you to put the hot spot of the light where it is centered around the front sight of the weapon the first time every time.
Weaknesses
The Rogers technique is probably the most difficult hand-held light technique to master. When you first try it out it is probably the most awkward and unnatural feeling technique you will try.
On some weapons the Rogers technique can interfere with the function of the weapon. It's particularly bad about ejecting magazines on some semi-autos.
While you can use the Rogers technique with many flashlights, it really does work best with lights dedicated to the technique like the 6Z/Z2 combat lights discussed earlier.
People usually require A LOT of practice to get the light indexed with the sights using this technique. Generally they end up pointing the light at the ground or way up in the air while the sights are more or less on target until they've mastered the technique.