How do I make a Pokemon stronger?

I recently caught a rather low-CP Growlithe, and I want to make him stronger, either through increasing his CP or by evolving him.

What can I do?

You may use Candies and Stardust to strengthen and optionally evolve Pokemon, with Stardust only being needed to power up a Pokemon.

Pokemon Candies are restricted to the "family" of Pokemon that they are designated for. You may get these by capturing Pokemon of the same family (for example, a Beedrill will give you Weedle candy), or by Transferring a Pokemon of the same family to the Professor.

You may get Stardust from capturing any Pokemon, and from the Defender Bonus available to players every 20 or so hours.

Once you have enough of both items, you can tap the Power Up button on the Pokemon's screen (see below picture) to increase both their CP and their HP. You may do this repeatedly until you reach a predetermined CP cap (based on your Trainer Level). You will be aware of reaching this cap because the semicircle will be full, and you will get an error on trying to further "power up" your Pokemon. To bypass this cap, simply level up your Trainer and try again.