To equip an item, simply right click the item and a GUI will appear with a list of Pokémon that can use that item, or you can throw out your Pokémon (right click the Pokémon you are holding) and then right click the Pokémon while holding the item you want to equip.
To remove an item, SHIFT CLICK on the Pokémon while your inventory is open, this will open a menu for your Pokémon and you will then click the item you want to remove. (Please note: you cannot equip items from this menu.)