Evolution is when Pokémon transform to other species, exclusive to their evolution lines. There are some ways by which it happens.
Ways of evolution[edit]
Leveling-up[edit]
Sometimes when a Pokémon levels up, it evolves. To grow levels, your Pokémon must get a certain amount of experience points. The experience it gains causes it to gradually mature until it finally wants to evolve.
To cancel Pokémon's evolution until the next level-up, repeatedly tap the 
button during evolution, or have the Pokémon hold an Everstone. This is useful for Pokémon to learn a move that its evolution won't or only learns much later. Preventing a Pokémon to evolve will affect its stat growth only while it remains unevolved. Once it evolves, its stats will increase to the level it would have had as if it had evolved at its proper level.
Leveling-up with high friendship[edit]
Some Pokémon only evolve when leveling up if their friendship level is high, past a certain amount. This is a more modern way of Pokémon evolution where Pokémon need to have bonded with their trainer. It allows Pokémon to evolve at unusually early levels. An example is Chansey evolving into Blissey. Daisy, from Pallet Town, roughly tells players how friendly their Pokémon are. However, if the player has not obtained the National Dex and the player’s Pokémon’s friendship level is high, the Pokémon will go into the evolution screen and it’ll stop evolving. An example is Golbat evolving into Crobat.
Trading[edit]
Using a GBA link cable you can trade certain Pokémon to other trainers. Some Pokémon evolve when this happens. An example is Kadabra, evolving into to Alakazam.
Trading while holding an item[edit]
Some Pokémon evolve when traded while holding an item, which is also another more modern method of evolution. An example is Scyther, which evolves into Scizor if it's traded while holding a Metal Coat. However, there are certain Pokémon that will stop evolving during trade due to the fact that the player has not beaten the Elite Four or has not got the National Dex. An example is Onix evolving into Steelix.
Evolutionary stones[edit]
Leaf, Sun, Moon, Fire, Thunder, and Water stones also evolve Pokémon. An example is using a Water Stone on Staryu, so that it evolves into Starmie. Evolution stones allow Pokémon to evolve at unusually early levels.
Other ways[edit]
Other ways of evolution belong to other Pokémon games and it's important to know that they will not work in the game that you are playing, which is FireRed and LeafGreen. Make sure that the evolution method belongs to the game being played but also that the evolved Pokémon exists in these games, as some evolved Pokémon may have been created only after these games were already made, thus being impossible to appear on it.
Branched Evolution[edit]
Branched evolution is a trait of Pokémon that can evolve into one of several possibilities. Eevee is the flagship of this method. It can evolve with at least three different evolutionary stones, each resulting in a different species.
Obtaining Pokémon evolution lines backwards[edit]
Some Pokémon can only be obtained already evolved. To get their unevolved forms, breeding and holding items is required. Breeding is enabled towards the end of the game, but is left largely unexplained in-game, confusingly. By breeding, Pokémon essentially mate and produce an offspring. The offspring might be unevolved, especially if the Pokémon breed while holding certain items.