My touring thus far has been two days with an overnight ~90 from home. But I regularly do 200K brevets and even a 300K brevet. To build up to 300K in a single day (these events have time constraints, albeit generous ones ~10mph avg including stops), I did several weekends where I rode 200K on Saturday and then a 100K on Sunday.
For one ~80 mile permanent that went up Reddish Knob in Virginia (6 miles sustained climbing at 8-10% grade) this flatlander put time in on the stationary bike at the gym which gave me an approximation of my wattage. I worked up to 2@20 minute sessions sustaining what an online calculator claimed was the wattage I need to haul me and my bike up that grade. That ride up Reddish Knob was the hardest thing I've ever done but I didn't stop, didn't topple over, and didn't walk. The views were incredible! I really had to push the remainder of that route since I was so slow going up the mountain that I was way behind when I got back down into the valley in West Virginia.
Last spring I rode 3 permanents (100-120K each) in different states out east (collecting states for an American Explorer award) along with a 200K brevet, a 10 mile hike in Shenandoah National Park, and another hilly ~120K perm. That was 6 straight days of challenging physical activity. I was most concerned about any issues with my saddle but all turned out fine.
I typically can only ride on weekends due to the work constraints but I do get to the fitness center every morning and I'm no stranger to the weight room.
So to echo what others have said, if you keep a certain base level of fitness as well as have realistic expectations of daily touring mileage, you don't really need special training (barring terrain you aren't usually riding!). I also found it helpful for my recent mini-tour to have ridden my bike several times prior fully loaded so that I could get a feel for how it handled as well as make a few tweaks to my setup/packing.