How do I evolve in pokemon in super mystery dungeon?

You can't evolve in Pokémon Super Mystery Dungeon until you have entered into the epilogue portion of the game which is after defeating the Final Boss after you have went through the Tree of Life dungeons at which point you can talk to Lapras and select "Visit the remote parts of the world" and then select "Sea of Wonders" and then select "Tree of Life" and then talk to Xerneas to start the evolution selection process however there are some Pokémon that even though they should be able to evolve you will not be allowed to evolve them and in terms of your Starter and Partner you will not be able to evolve them until after you have cleared the Mew portion of the epilogue chapter which includes finding a sleeping Mew in the Purifying Cave however once you leave the Purifying Cave you will be able to evolve your Starter and Partner. Also Pokémon that require specific things such as items, happiness or to be traded most will not require those specific things so in order to evolve someone like Azurill you can evolve it at any point.