Before starting the battle, if you check the Pokedex, you have two options under the Pokemon - Power Up and Evolve. The difference between buffing and evolving a Pokémon is that evolution completely changes it, including its appearance, and the amplifier increases basic stats, such as Combat Points.
Another difference between the two is that you need stardust to increase the power. Evolution requires another resource - candy. While both of these items don't matter much at the start of the game, you'll soon realize that these are probably the most important items to stock up on in Pokemon GO.
Once you have enough candy, you just need to select the Evolve option, which will not only give you some experience points (XP), but develop your Pokémon into a more powerful one. If your Pokémon evolves into a new species that you haven’t met before, you will receive a bonus experience.
The last thing you need to know is Stardust is versatile and can be used to power any Pokémon. Candy, in turn, is a specialized resource, and each Pokémon needs a different type of candy in order to evolve.
Materials on the topic:
How to get stardust
How to get candy
