I went a couple years ago. There are two ways an average person can take a car out on the 'Ring: either as part of a "Tourist Day" which happens almost daily or a "Track Day" which happen less frequently. My brother and I chose the latter.
We rented a race-prepped Suzuki Swift from Rent4Ring, I would highly recommend this place for anyone interested going in the future. They did an excellent job of taking our booking while we were still on the other side of the world without even a deposit. They also did an excellent job of preparing the group of us renting race cars before going out by playing a video and pointing out certain corners and sections of the track to look out for.
I think a track day is the better way of going out on the 'Ring, even for someone with minimal track driving experience. They day cost us about $600 Euro and included 10 laps. Extra laps were $50 Euro I think. There were about 5 of us renting and another 5 private drivers at the event. With only 10 cars sharing the entire 'Ring, My brother and I practically had it to ourselves whenever we were out! Only the occasional 911 or GT-R passing us once in a while.
As soon as our day ended at 5 pm, a Tourist Day began, there were probably 100 drivers waiting to go out. I can only imagine how crowded it would have been out there. All that traffic at high speed is what makes track driving intimidating to beginners, that's part of the reason I say the Track Day was better. Another reason is that during a Tourist Day, drivers must treat the 'Ring as a road: you can only pass on the left (which is off of the racing line for essentially half of the track) and there are speed limits in certain sections. The last reason is that during a Tourist Day drivers cannot use the full straight-away. This is because of the pay-per-lap system: drivers enter the track at the end of the straight and exit at the beginning. Drivers are not forced to exit during a Track Day and so they have full access to the track with no restrictions.
I'll never forget having that little Suzuki pegged in 5th gear down the main straight-away at 120 mph with 911's and GT-R's flying by at 200 mph! I can't wait to go back and rent a more powerful car!
Anyways, just wanted to share my experience, hope some of the info helps!