There are various ways to Tame the Digimon in Digimobs. In the current release (0.8.1), it is possible to tame Digimon in only 2 ways. In previous versions there were other tested methods which may or may not return in future updates.
Current 0.8.1 methods :
Whilst wandering through the world of Minecraft with Digimobs installed, you may come across Acorns. Or if you happen to kill a Digimon, it may drop some.
Holding these the Digimon will follow you, but if you right-click an un-tamed Digimon, it will eat it. After a fair amount of these the Digimon may become tamed.
The D-Power is an item that when right clicking on a Digimon, will instantly tame them. There is no damage value to the D-Power so it can be used constantly to tame as many Digimon as you wish. This item is un-craftable and is obtainable only in creative mode.
After Taming ?Edit
After Taming a Digimon, what do you do next? Well, you can craft a Datalink Digivice so that you can check thier stats, or to re-name them, comes in handy for other things too.