Startdust is used commonly to power up every Pokemon.
How to get Stardust
Capturing wild Pokemon
Hatching Pokemon Egg
Candy
Candy has the name of Pokemon and can be used to certain Pokemon and its 1st- and 2nd- evolution Pokemon. Candy is needed for power-up and evolution. Ex) Pidgey Candy is used to power up Pidgeotto and Pidgeot.
How to get Candy
Capturing wild Pokemon
Hatching Pokemon Egg
Transferring Pokemon to Professor Willoww
Tips for using Stardust & Cnady
Using Candy for Evolution preferably
Since moves Pokemon have changes by evolution, evolving Pokemon before powering up is the best to find the most powerful Pokemon.
Selecting Pokemon with higher CP to power up
CP, the stat Pokemon have in Pokemon Go, indicates how powerful the Pokemon is. Pokemon with higher CP should be powered up by spending Stardust and Candy.
Where to get Stardust & Cnady
Catching Pokemon
You need to catch wild Pokemon as much as you can to earn Stardust and Candy. You can get more Candy by transferring Pokemon to Professor Willow.
Hatching Pokemon Eggs
Hatching Pokemon Eggs is one of the resource of Stardust and Candy. You can get Stardust and Candy slightly a lot relative to other ways.
Transferring Pokemon to Professor Willow
By transferring Pokemon to the Professor, you can get Candy of Pokemon transferred. Note that you cannot take transferred Pokemon back.