I've modeled a Revolver and I'm adding an armature modifier to it. But in the Object selection area it isn't there so I can't do anything
You have to have an armature in your scene before adding an armature modifier. You add an armature to your scene the same way as adding other types of objects, with Shift-a, for add.
Once your armature exists, then when you try to create the armature modifier, you will find that your armature is available for selection in the field that requires an armature to be specified.
Note that directly creating an armature modifier isn't strictly necessary, because there is an alternative means available for creating the needed connections. You could get the same results by simply selecting your mesh, shift + selecting your armature (to add this armature to the same selection), then parent (with Ctrl-p) the mesh to the armature. Choose Armature Deform from the drop-down, and finally, choose a bind method, such as Automatic Weights or Envelope Weights. Following these steps will create an armature modifier automatically.