Successfully complete the indicated task to change forms:

Arceus: Give a plate to Arceus to have it change form.
Deerling and Sawsbuck: Deerling and Sawsbuck will change into their Spring, Summer, Fall, and Winter forms depending on the current season based on the system time.
Deoxys: Examine the meteor in the museum in Nacrene to cycle through Deoxys' Normal, Attack, Defense, and Speed forms.
Eevee: Fight enemies near the moss-covered stone in Pinwheel Forest to evolve into Leafeon. Fight enemies near the frozen ice crystal at the bottom of Twist Mountain to evolve into Glaceon.
Feebas: Trade Feebas while it is holding a Prism Scale (obtained on Route 13) to evolve into Milotic.
Giratina: Give Giratina a Griseous Orb from the Shadow Triad on the Marvelous Bridge to change into its Origin form.
Karrablast and Shelmet: To evolve Karrablast and Shelmet, trade one for the other with another player. The Karrablast will evolve into Escavalier and the Shelmet will evolve into Accelgor.
Magneton: Fight enemies in Chargestone Cave to evolve into Magnezone.
Nosepass: Fight enemies in Chargestone Cave to evolve into Probopass.
Rotom: Open the boxes in the first door on Floor 1 of Shopping Mall Nine to change into Rotom's Normal, Heat, Wash, Frost, Fan, and Mow forms.
Shaymin: Give a Gracidea (from the woman in the Pokemon Center in Lacunosa Town) to Shaymin to change it into its Sky form.