AtmosMobs 2.0 is a whole new re-write of AtmosMobs intended for the 1.6.4 versions (and possibly 1.7.2 versions as well). This version includes new behaviour, new mob models, and new mechanics, specifically for taming.
See the list of mobs coming for 2.0.
There are different mechanics for each type of mob.
Land Creature: In order to tame the more mammalian land creatures, you must gain their trust, and after a while, they will warm up to you. All land creatures are also able to breed on their own.
Insect: You could catch them in bug nets, as well as put them in jars/bug display blocks.
Fish: In order to to tame one, you must catch it with a fishing net.
Bird: In order to tame one, you must hatch it from an egg. They will also build nests and put their eggs in them.
Build 1: It is unknown when the first build will be released, however, it is possible that it might be released in May or June. The preliminary mobs in this build will be the Butterfly, Chameleon, and Fox.