What @schoolmedsboi described is 100% accurate. The actual time when you're penetrated by a finger isn't long, anywhere from 5 to 15 seconds.
As far as positions, the basic ones that I've had are:
1) On the table on my left side with my right leg pulled up. I absolutely hate that position because it's just not that comfortable for me.
2) Standing and bent over the side of the table, resting my forearms on the table with my head down. That position is probably the most common and it's OK but not fantastic.
3) An alternate to #2 is standing on the little step that pulls out on the front of the exam table (used to help you get on the table). Then bent over like #2. In this position, your ass is much higher and your head is down at a sharper angle. I like this variation a little bit better than #2 (more exposed).
4) On your knees on the exam table. Resting your upper body on your forearms, hands, or elbows. Or your entire upper chest and head may be completely down on the table. In any case, your ass is up high and the doctor/nurse can see everything. This position is not that common because most practitioners feel that males will be embarrassed to get into this position. But it's my favorite and I ask for it any chance that I get. My PCP knows that this is my preferred position now and she readily tells me to get into this position when it's time for my rectal/prostate exam.
If you want to try #4, just suggest to your doctor that you've had the exam done in this position before and it's the most comfortable for you. You can also tell them that in the past you've had a DRE and the doctor who did it had trouble reaching your prostate and that they were able to examine you better in this position. That usually works.
And yes, it's usually (always) only a single finger that's inserted. The free hand of the doctor is usually placed on your exposed butt cheek while the index finger that is about to penetrate you is well lubed. They will then use their thumb and middle finger to spread your cheeks slightly while the index finger is inserted.
Good times!