Blender - Give armature bones influence over an object

To create animations and poses with an armature first you need to give it control over an object. Start by selecting only the object you want the armature to influence. Next control+select the armature so you have both the object and armature selected. Finally go to object->parent->with automatic weights. This option will set the object as a child of the armature and automatically apply bone influence weighting. You can go back and change the weighting manually later if you desire.

The result of the parenting is the object is now the child of the armature. If the armature is the child of the object then the armature bones will have no influence over the object. In this case you probably selected the objects in the wrong order before parenting. The end result in the scene collection should look like the image below.