DRE is not a major big deal.
As most have said, the most common position is leaning over the end of the table, but possibly in the Sims (on your side, left knee to your chest, facing away from the doc.) or on all fours on the table. (It's usually the doctor's preference, but some clinics may have a certain SOP)
The lube will feel cold, and, if you have never had one before, it may be a tad uncomfortable at first, but once you get use to the finger in your butt, it's not bad. IF the exam is done right (that is, not too quickly) you may feel pressure in your penis like you are going to ejaculate. THIS IS NORMAL! The main function of the prostate is to supply the bulk of the liquid portion of semen, and during ejaculation it contracts to push the fluid into the urethra, so if the doctor is putting pressure on your prostate, it is logical that you may feel like you will ejaculate. Some fluid may be expressed, either intentionally or accidentally from the head of the penis. Again, it is nothing to be embarrassed about. If the doctor has expressed the fluid intentionally, he/she will probably collect some on a microscope slide. Either way, they will hand you a tissue after it is all done to wipe both the head of the penis (if necessary) and the excess lube from your rectum.
My personal experience has been that female doctors do a more thorough and gentle job than males.
The whole key is to relax. the more relaxed you are, the easier the exam will go. It's all over in less than a minute.