First obtain a digi-egg through matching. And follow these simple steps:
1) View the hatching requirements for the egg...
Ex: Green Digiegg- 500+ Insect Exp.
2) Meet the requirements!
To earn Exp. for the egg just put it in the corresponding farm.
Ex: Green DigiEgg- 500+ Insect Exp. goes into a insect DigiFarm.
3) Meet the requirements? Time to hatch 'em!
Once you've met the requirements 'Talk'/click on your DigiEgg.
4) Start training your brand new Digimon and enjoy.
5) -optional- Get more of a certain Exp.
Just put a farm good that will do that... like a cathedral for more Holy Exp.
Other Requirements:
If it's on a stat like say HP use the training option.
Like a treadmil will give you an HPCHIP thing to use on your digimon.