Understanding Texture Atlasing

I've been trying to read up on how to create and use texture atlases but there doesn't seem to be any good starting resources - most just say make it in your 3D program without explaining how...

Desc of our project:

• 2D tile based city destruction game

• developed for mobile (initially iOS)

• Currently we are using mesh planes generated in MAYA and applying textures/materials in unity with scripts to create game object prefabs

• 4 plane mesh sizes: 64x64, 128x64, 64x128 and 128x128 (we use multiple meshes for our level generation scripts)

• The shader setting for all of our meshes/textures is unlit transparent

• Each game object needs to swap textures to multiple damaged and destroyed states for game play - we have a texture variation for each.

I don't quite understand the best way to make a texture atlas for our project (its all new to me) so any help would be greatly appreciated!