Instructions
Open your list of Pokémon and select an unevolved creature you want to hold a big mushroom. Remove any items the Pokémon may currently be holding.
Select the option to assign an item to that Pokémon and scroll through your list of items until you reach the big mushroom, an item that has no real function besides being able to be sold to Pokémon shops for extra money. Assign it to your Pokémon to make them hold the item.
Evolve the Pokémon by doing the necessary tasks needed to achieve this. Every Pokémon evolves differently, but most evolve after accruing enough experience points to reach a certain level. The specific level you must reach varies wildly from Pokémon to Pokémon. Use your Pokémon in battles against other trainers and wild Pokémon to get more "EXP." Eventually, they will evolve into their next form with the big mushroom.