Power Up Your Pokemon
Powering Up requires a mix of Stardust and Candy. Stardust can be used for any Pokemon whereas Candy is species specific. Powering Up will usually require a single Candy, but will require more depending on how close the Pokemon is to reaching its full potential, regardless of its evolution stage. You can tell how close a Pokemon is to being max CP by the white, half circular bar. Usually, once the bar is 75 percent of the way, it will start costing two Candy. Amount of Stardust needed to power up a Pokemon will depend on species and scale with that Pokemon's CP. Powering up will increase that Pokemon's CP and HP.
You'll find that your Trainer level will limit the amount you can increase your Pokemon's CP. If you try to Power Up your Pokemon beyond the white bar's limit, you'll get a notification that your Trainer level isn't high enough. Once you level up your Trainer, you'll be able to Power Up your Pokemon again!
To evolve your Pokemon you must have the specific type and necessary number of Candy, which will enable the evolve button.
Evolving your Pokemon is a sure-fire way to drastically increase your Pokemon's CP in one go, but this could require quite a few captures. This Pidgeotto needs 50 Pidgey Candy to evolve. Since each Pidgey capture awards you with three Candy and each transfer with one, you need to catch 13 Pokemon from the Pidgey evolution line before you'll be able to evolve it.
Some Pokemon, like Magikarp, need a huge number of Candy before it will evolve. To get a mighty Gyarados you'll need 400 Magikarp Candy!
Evolving your Pokemon has a few effects besides making it stronger. Your newly evolved Pokemon will be fully healed, and its moves will be randomly re-selected. Because of this, don't choose which Pokemon you want to evolve based on the moves it knows. They'll probably change anyway!
Additionally, evolving your Pokemon grants you 500 XP. Evolving it into a Pokemon you havent caught before? You get an extra 500 XP bonus--a total of 1000 XP for your Trainer!