To use an evolution stone, simply go to your inventory, select the stone, and then use it on the Pokemon you want to evolve.
Some Pokemon, such as Eevee, can change form by being exposed to certain conditions. For example, if you expose Eevee to a Thunder Stone, it will evolve into Jolteon.
Finally, some Pokemon, such as Rotom, can change form by using different appliances. For example, if you use the Fan Rotom on Rotom, it will change into Fan Rotom.