Anyone can don armor or hold a Shield, but only those with training can use them effectively, as explained below. A character’s class and other features determine the character’s armor training. A monster has training with any armor in its stat block.
If you wear Light, Medium, or Heavy armor and lack training with it, you have Disadvantage on any D20 Test that involves Strength or Dexterity, and you can’t cast spells.
You gain the Armor Class benefit of a Shield only if you have training with it.