It's really quite simple, TBH.
You select your egg in the incubator, then hit "Data Input" and it'll use up the corresponding data you have in your inventory. Different Digimon require different amounts of data (and obviously different types).
When you input data there's a 50/50 chance of success/failure, and if you fail, there's a chance the egg will break and you'll need to get a new one and start again.
You need to input data 3 times to be able to hatch the egg, but you can input it up to 5 times (but obviously, that's more chances to break).
If you input data 4/5 times, your Digimon will be bigger and have better stats than if you hatched at 3/5, and if you manage by some miracle, to get a 5/5, it'll be the biggest it can be and have the best stats it can have. :D
Edit: And as much of a pain as it sounds to get the best stats, it's still a million times easier than attempting the same thing on Pokemon games. :x
Cool. Back to collecting Boarmon poop for the dodgy doctor guy. :|