How do I enter Pose Mode in Blender 2.81? I have a figure and added rigging.

I'm supposed to select both objects, go to auto weights and then switch over to Pose Mode.

I don't see that option. How do I pose my character?
What most likely happened is that you have the deforming object controlled by the bones selected as active. Select only the bones, and switch to pose mode. You don't need both selected.