I'm going to answer this as a true couch to century with a general plan. You can write books on this stuff. There have been books written on this stuff.
You have three major goals for a successful century:
- Get the raw fitness needed to keep the pedals going for 6+ hours.
- Figure out how much you need to eat while going for the entire thing.
- Do the above without getting any stress injuries.
Off the Couch
You are off the couch. You have a bike, old, new, mountain bike, road bike, it doesn't matter. If you've never ridden, get something cheap so you're not out much money if this isn't for you. You have at least one pair of cycling shorts, gloves and a helmet. The goals here are just to ride around. Don't go terribly hard, find some scenic routes, avoid steep hills if possible. Most importantly, work on pedalling smoothly. Nice circles with the feet.
Each week, try to get in three one hour rides.
Building up
Make your way up to 4 rides per week. Three shorter ones and one longer one, maybe up to 2 hours. On your favourite loop, you'll see your average times slowly dropping. You are still not trying to ride really hard. When you get to the point that your weekly 2 hour ride isn't leaving you wasted for the day and the century still seems like a good idea, it's time for the next phase.
Really Starting
Get a road or touring bike. Mountain bikes were fine up until this point, but unless your century is off road, you will want a real road bike. Get fitted by a pro, this is possibly your single biggest injury prevention mechanism. Get clipless pedals. Practice with them on the grass until you stop falling over.
The following sections can be repeated as needed. I did not get to 'month 3' for at least a year. Listen to your body.
Month 1
If you commute by bike, everything other than the 'long' ride could be 2 shorter rides, always work on smooth pedalling. For the longer ride, bring a small snack and practice eating.
Week 1-2: 3x1 hour, 1x2 hours
Week 3: 3x1 hour, 1x3 hours
Week 4: 4x1 hour
Month 2
Once per week, on the one hour ride, spend about 20 minutes in a flatter section riding harder. You want to hit a pace that's uncomfortable, but when 20 minutes is up, you can keep riding. You're not killing yourself here. You should be breathing hard, but if you really had to, you could go at that pace for an hour or more. This will take practice.
The longer rides now provide the constant threat of bonking. Try out gels, sports drinks, bananas, cold roasted potatoes and see what is palatable for you on the ride. Most organized centuries have food stops, so you need to know before you do it if the food they are going to provide will agree with you. Aim for ~300 calories per hour, but listen to your body.
Week 1-2: 3x1 hour, 1x3 hours
Week 3: 3x1 hour, 1x4 hours
Week 4: 4x1 hour
Month 3
Once per week on a one hour ride, do 2 of those 20 minute efforts with a 10 minute gap in the middle. Again, you're not killing yourself on these. It's uncomfortable, your legs are telling you that it would be nice to slow down a bit, but you can tell them to shut up. Put one or two similar sections into the longer rides.
Week 1-2: 3x1 hour, 1x4 hours
Week 3: 3x1 hour, 1x5 hours
Week 4: 4x1 hour
Century
Once you are capable of a 5 hour ride, assuming that's not already century distance at your speed, you will effectively be capable of riding for 100 miles. It's just a matter of continuing to eat, drink and keep the pedals going.
Notes
Listen to your knees and joints. You will get more supple on the bike and you may need to get fitted again several months in. Fortunately, after that, you shouldn't change much.
