Power up

Power Up is a game mechanic in Pokémon Go that allows the player to strengthen their Pokémon by increasing their CP level.

Powering Up or leveling up Pokémon involves two items, Stardust and Candy. Fortunately these two resources are gathered simply from catching Pokemon.

How to Power Up
From the Pokemon menu, select a Pokemon you wish to Power Up. If you have the required Candy and Stardust, simply tap Power Up to increase your Pokémon's CP level. Your resources will be consumed and your Pokémon's CP level will increase. Most Pokémon award you with three of their specific candies when captured, meaning you can level up a Pokémon 3 times if it's the only one you've captured. Additional Candy can be acquired from duplicate Pokémon captures.

Stardust
Stardust is obtained by catching Pokemon or holding a Gym location for a fixed amount of time. Stardust is used to Power Up your Pokémons' CP level.

Candy
Candy is a Pokémon specific item used to evolve your evolution-capable Pokémon, usually at a cost of 25 to 50 candy per evolution. Evolving a Pokémon results in an immediate CP boost. A single piece of Pokémon specific candy is also required for a basic CP Power Up.