I don't understand how stardust works on Pokemon GO. It says I have 7658 stardust but I can't do anything with it. Won't allow me to power up anymore even though I have so much of it remaining?
You get candy by capturing pokemon. If you capture a pidgey you get 3 pidgey candy. In addition all evolutions of the base pokemon gives the base pokemon's candy. So a pidgeotto and pidgeot will also only give 3 pidgey candies per capture however pidgey, pidgeotto, and pidgeot all use pidgey candy to power up. Also transferring a pokemon gives one candy.
In order to use stardust you have to have the candy to powerup the pokemon.
In addition to the other two answers, you may run into a power-up ceiling based on your user level. I know I powered up a Hypno, still had enough stardust AND candy to continue, but was told my user level was too low to continue powering it up, even though it hadn't reached the maximum displayed in the half-circle CP bar.
Stardust is the key to playing the game. The motto "gotta catch em all" stands true, because even if you are leveling up a Dragonite, you still have to catch Pidgeys and Zubats just for their stardust. You may only want a strong Arcanine, Dragonite, or even Charizard... but the amount of stardust you will get from catching only that species, because it is somewhat rare, will take you FOREVER! you get 100 dust per capture, and 3 candies. just to get a Charizard, you would mathematically have to catch 32 Charmander, which would only give you 3200 dust. and once your pokemon CP gets and level semi circle behind them gets high, that isnt enough to do anything.
Candies = Needed for an individual species of Pokemon to level up and evolve. Can only be acquired by catching that species or hatching that species from an egg.
Stardust = Needed strictly to level up ANY Pokemon (in addition to the candies). Can be acquired through catching AND hatching ANY species of Pokemon. Needed to level up the CP of your Pokemon which increases their base stats including HP, ATK, DEF, and STMA.
Just catch every Pokemon you come across. You'll get to a point where 50k stardust still isnt enough. Trust me.