It is also common to keep the facial features as separate objects, and you can certainly use one armature to control multiple objects. The 2 most typical ways to do it is:
1)[SEPARATE OBJECTS] To have one of your bones (the head bone usually) have complete control over the features. In this case the features would all move as a whole following the head bone, and further movement (e.g. eye rotation is done via keyframing the objects loc/rot. To do this you would: select the armature, and in pose mode select the head bone (And only the head bone, so it is slected and teal) in object mode select one eye. holding shift select all the other facial features. Still holding shift select the armature last. Let go of shift, hit ctrl P and choose 'bone'
2)[ONE JOINED OBJECT] Join the meshes as suggested above. Then create separate bones for each feature. each of these bones is a child of the head bone in the armature hierarchy. each of these bones (e.g. bone.eye.L) has complete control of the feature using vertex group.