So first you need to move the object to the the class library then save it as OBJ file. . it can be a source or a frame or any object. but it has to be in th class library. in the below picture i have shown that i can save a source object as a *.obj file and then i can load it again in different model.
Instead of saving the object, saving it as a library would be better. To do so you got to select the right click option 'Make Library' and then you can enter in information about the library, then when your ready to save it then right click -> Save/Load -> Save Library As and then you can update the library information before you save it.
The benfit of using a library is you get the ability to easily update the objects within your models with the new updated object. You will find in your preferances a setting as to where your libraries are located, set this to a folder you want to use and store all of your libraries in there and then you can use the library manager to add any of the libraries to your models or to update any libraries (you are notfied within 30 mins of updating a library about a higher version being avalibe).
Also you can store multiple versions of the same library and swap between them by saving them under a different filename but in the same folder with only changing the version number on the library information.