I haven't done back to back centuries, but I do the Horsey Hundred in eastern Kentucky each year. Last year I rode 110 miles on Saturday and another 70 miles on Sunday at a decent clip. Both days are pretty hilly. I also do some weeklong tours, although the mileage each day is usually in the 65-85 mile range.
With respect to training, do as many back-to-back long rides as you can.
Also, stay on top of your hydration as best you can. Try to drink more than you usually do. If you're like me, you will be beyond hungry. Eat and then eat some more. It's not the time to count calories!
Make sure you address well in advance of the ride any fit issues that you're having with your bike. Also make sure you have two pairs of good long-distance shorts and that you use (and carry during the ride for reapplication) some chamois cream. No matter how many miles you have in, your booty will probably hurt. I've had some of my only saddle sore issues after the Horsey. I find that zit cream is the best treatment for them once they have developed.
Live with intention. Walk to the edge. Listen hard. Practice wellness. Play with abandon. Laugh. Choose with no regret. Continue to learn. Appreciate your friends. Do what you love. Live as if this is all there is.
--Mary Anne Radmacher