About 90% of my shooting is from the prone position, as follows.
My right hand (I'm right handed and right eye dominant) loosely holds the palm swell, there is no real grip and I don't worry about the rifle getting away from me. I have some "non-skid" tape type stuff on the palm swell, it's cut into small pieces and placed under the positions that my finger tips and thumb occupy when properly positioned, this gives me a good tactile feel for when I'm properly positioned (It's just for positioning when shooting prone but provides a good grip surface when shooting "off-hand").
My right cheek is loosely on the rifle, I have a pad to adjust the comb height. I like the comb high enough so that while completely relaxed on the stock my eye is still centered on the scope. Basically, I could sleep in the prone position with my head on the rifle and still have a perfect sight picture when I open my eyes.
My left hand DOES NOT touch the rifle, it's on the sand sock that's UNDER the butt of the rifle, the sand sock is not at any time between the butt plate and my shoulder, it's not a recoil absorbsion device.
I apply enough shoulder pressure on the rifle butt to take the slack out of the bipod system. I don't tense-up but stay completely relaxed and "ride" with the rifle's recoil, sort of "free recoil" but my shoulder actually touches the rifle. I feel this forward pressure is necessary as it allows the me to control ALL points of pressure on the rifle. I believe that by not "loading" the bipod there is an unknown introduced, the unknown being the amount of recoil travel before all surfaces make contact.
I shoot ALL rifles in this manner, even the heavy recoil 338 Lapua and 338 RUM with the 300 Sierras.
I position my body directly (or as near directly as possible) behind and in-line with the rifle. This reduces some of the torquing that occurs when the shooter is positioned at an angle behind the rifle. Also, I feel that when shooting in the in-line manner the rifle returns to zero in most cases unlike the sideways jump usually experienced when shooting with an angled position. The shoulder MUST be positioned in the same place on the butt plate for ALL shots. We know about the "pocket" on the shoulder and placing the butt firmly there but the position I'm refering to is the shoulders' position reletive to the toe and heel. If the shoulder is too low on the butt and the contact is mainly on the "toe" of the butt the rifle will recoil with a bit more upward movement "jump", I prefer to have the butt a little low and have a bit more "heel" on my shoulder, this I feel make the rifle recoil straight to the rear and reduces "jump". However it's placed on and in the shoulder the butt pressure and position my be consistent.
Here's a photo of a good in-line position behind the rifle, notice no left hand on the rifle.