It can be in anyway you want, since it depends on the engine/editor's features.
As for implementation, let's say you pick the FBX format. First, it's different from OBJ because it can also export animations, and a bunch of more informations. You also have the option of exporting it in ASCII for easier reading and see what you have available, but you can also export it in binary and use a binary reader (ex. notepad++).
After reading the file content's, you'll know what information you have available there. There's a bunch of numbers, some characters, etc... then it's time to figure these values out. You can google, and you can export different models, comparing values and figuring what each value means.
With that information fully figured out you are able to build the exact scene you exported from your 3D modeling program in your engine/editor.
You should take note, however, that even though you can achieve the same results through different techniques, it doesn't mean they're the same.
For example, if you animate a mesh by moving it's vertex each frame, you'll have this information in the file in a specific manner, and your engine/editor should be able to read it and duplicate it if you want it in your game. If you animate it using bones but you do the exact same thing, the information will be different so you'll have to make your engine/editor be able to read this as well.
If it's your first game though, I think it's better to define a single method, and work with it until the end, such as "for animated models, they must be Editable Meshes and have SkinWrap and Bones", so you can focus on working on the game than creating readers and figuring all sorts of possible information from the 3d program you choose.