I have already answered to this question when I have related my first visual inspection of the rectum since both happened at the same physical examination but the prostate exam was more a surprise for me
it was during my physical examination by a military doctor in group at a pre-induction militarry center at 18 age for the mandatory military service
It was the last part of all the examination
The doctor first instructed us to turn around ,to bend over and to spread our butts and he looked inside the asshole and around with a kind of flashlight
then we were instructed to get up on all fours on a medical table and without any explanations he instructed us tospread our feet and to lean the shoulders and face towards the table with our butts in the air, he told us to relax and without warning he inserted his finger in our rectum brutally and turned it on all sides and then went deeper before removing it, He gave us a strong smack on our butts and then instructed us to climb down of the table and to stand up again
It was unpleasant because he was very authoritarian and barked after us if we moved a little or complained.
He did not use a glove but washed his hands after each guy
It was for me the first time and It was only after that a guy explained me why he was doing that even if he did not know himself exactly.
When I was inducted in barracks, at my first physical examination one day after our arrival an other military doctor gave all a group of twenty recruits a complete examination which included again a DRE.
It was almost the same, also brutally performed, but that time he explained us before when a small group was standing in front of him near the medical table the reasons of that exam. To make us relax, he gave each of us a smack on the butts before inserting his finger and annother after.
I have had several DRE later since I reached 40 age but performed more slower by private doctors at their office or at medical centers always with gloves.
But for the position, it was generally on all fours ( one doctor told me that it was the less comfortable for the patient but the best convenient for the doctor) except for some doctors who did it while you were on your back on the table with the legs lifted and spread widely and knees on your chest to let the asshole very visible.
The position on the side is of course less embarrassing but it iis also the less convenient for a doctor.
A few doctors leave you the choice of the position