Evolution

Evolution is the first evolution in the Pokémon franchise when one Pokémon, upon reaching a certain level, using a certain stone, learning a certain move, or being traded, evolves into a different kind of Pokémon. In Pokémon Gold, Silver, Crystal, HeartGold and SoulSilver games, it says that Professor Elm is an expert on evolution and discovered that Pikachu evolves from  Pichu.

Normal Evolution Tricks
Pokémon gain experience after battling wild Pokémon and Pokémon Trainers. The more experience a Pokémon gains, the more it levels up. When a Pokémon reaches a particular level, it will evolve into its next form, if it has one. This is very helpful to most Trainers who want their Pokémon to become stronger.

There are ways to share experience, such as allow a Pokémon you wish it to evolve to hold Exp. Share. It is a hold item that allows the user to earn experience even if it did not participate in the battle. This is a convenient tool if you want to level up a new or low-level Pokémon.

You can prevent evolution by simply press the 'B' button on the Game when the Pokémon is attempting to evolve. This is useful as some Pokémon will learn moves that cannot be learnt in a later form or if you want a Pokémon to learn a move earlier than usual. For example, Gabite. If you let Gible evolve into Gabite at level 24 it will learn Dragon Rush at level 49, but if you keep Gible it will learn Dragon Rush at level 37. Sometimes it doesn't matter if you let it evolve or not. The Pokémon can hold an Everstone, which keeps them from evolving, so that you don't have to keep cancelling the evolution everytime the Pokémon levels up. However, if your Pokémon has evolved, it might not evolve again (Raticate, Linoone, etc.) Although some Pokémon can evolve more than once (Poliwhirl, Cascoon, etc.), some basic Pokémon just can't evolve, due to undiscovered forms, or if they are really rare (Chatot, Groudon, etc.) There are also Pokémon that can evolve into different things like love, choice, etc. For example, Eevee, Poliwhirl, Wurmple, or Kirlia.

Stone Evolutions
Some Pokémon will not evolve unless you use a special stone called an Evolution Stone. These special Items are linked to the Pokémon's type. Here are a list of Pokémon that can evolve by giving them the stones.

Item Evolutions
Some items are needed for a Pokémon to evolve. If a Pokémon hold the item allowing it to evolve, let it level up once and it will then evolve into the second form.

Trading Evolutions
A small group of Pokémon refuses to evolve, no matter if you are at the appropriate level to trigger the evolve process, unless you trade them with a friend. Some Pokémon need to have a held item to evolve when trading with a friend. Another group require specific Pokémon to be trade in order to evolve.

Gender Evolution
Small groups of Pokémon requires a gender to evolve into the next stage.

Friendship Evolutions
Certain Pokémon, especially baby Pokémon, requires friendship with its trainer and if they are fond enough, they are willing to evolve. Some Pokémon only evolves in a certain time of the day with friendship.

Location Based Evolutions
Special Pokémon evolve at a certain area of location.

Attack Based Evolutions
Certain Pokémon need to know a move to evolve. This method was introduced in Generation IV, starting with Diamond/Pearl/Platinum.

Unique Evolutions
Some Pokémon have certain type of unique way of evolve.

Mega Stone Evolutions
Certain Pokémon will be able to evolve into a Mega form, the final form for one-evolution families and second/true final form for two-evolution families with the use of a Mega Stone, a held object. However this evolution will devolve back into their previous form at the end of the battle.

Devolution
Devolution is a form of reverse evolution when a Pokemon reverts to a previous state. Devolution does not exist in the games but is common in the Manga and TCG. Devolution is achieved mainly unnaturaly - through experimentation, or Devolution Spray. Though certain Pokemon, such as Isamu's Clefairy and Pikachu are capable of devolving themselves. The TCG also has it that Eeveelutions can revert into Eevee and that Mew has two special attacks named the Devolution Beam and Devo Crush - both of which which devolves the Pokemon hit by the attack. Golurk and Jirachi also possess special attacks which allow them to devolve an opposing Pokemon.

Trivia
There are eight pokémon that can evolve into two different pokémon, but only two that evolve into more: Tyrogue and Eevee.