Some people might say that constant fighting and training caused Pokemon to evolve. This is true for most, however there are some that only evolve through special means such as special elemental stones and also trading the Pokemon back and forth. This is true, however I believe immense love and care towards Pokemon help too!
Pokemon evolve ounce they reach a certain level, also depending on how you treat the like EEVEE. Most pokemon have a hard time evolving thats why there are special stones to help the evolve, depending on wich game your playing. Also its good to keep them outside the pokeball.
Most pokemon evolve when they reach a certain level. However some, like Pikachu need a stone to evolve. These can be water, fire, electric, and moonstones. A couple can only evolve through trade like Kadabra.