When I was 15 a friend and I somehow convinced our parents to allow us to go touring for a week; we were Boy Scouts and I'd read a book on touring. We mounted racks and panniers on our cheap bikes, strapped a relatively-heavy tent down, and headed off. We hadn't trained particularly, other than being typical kids of the pre-internet era who pedaled all over town all day in the summer. We probably averaged about 40 miles per day on our tour, and we had many memorable adventures that make me smile to think about them even now ;)
Being middle-aged now, with a sedentary job, if I were to attempt a similar trip I'd have a much nicer touring bike and lighter gear, and I'd want to train for several months beforehand. It's one thing to be able to ride a bike loaded with 20 lbs of gear for many miles in a day, and it's another to be able to do that for several days in a row with only mild aches and pains. But you're not me; if you're younger and stronger, you might have no trouble just jumping on the bike and going. Also there's no rule about how far you must go in a day; personally I'd plan for about 50 miles per day on average (more on some days and zero on others), but if you and your friends want to just pedal lazily for two hours and then camp by the nearest swimming hole, then go ahead and do that.
One thing that I can say definitively is that in order for touring to be fun, you have to want to do it. The idea of pedaling a bike for a week straight should sound wonderful; it should excite you and fire your imagination.
The subject isn't often discussed here, but we hard-core bicyclists are a funny bunch. Just pedaling a bicycle, feeling the breeze in the face and leaning through curves, is fun for almost everyone able to do it. But pedaling hard or pedaling for a long time is painful. We hard-core bicyclists get a sort of runner's high, often attributed to endorphins, which is its own reward, and makes the pain worthwhile. Not everyone gets the same reward in the same proportion. That feeling, the many healthy benefits of the exercise, and the simple joy of riding (plus the desire for the respect of our riding peers, for those of us who ride in groups) is what motivates us to keep riding.
If you're considering whether touring is right for you, you might try training for a month. Ride at least two or three days a week. Work up to riding at least two hours in a session; you might have to start easy, as little as fifteen or thirty minutes, to get your body used to it. (Padded bicycling shorts help a lot; don't wear anything under them, or you'll have trouble with chafing.) Push yourself, not so hard that you can barely talk, but enough that you feel like you've accomplished something afterwards. At the end of the month, if you feel like the training was worth it and you want to continue, then you'd probably enjoy touring.