Eevee evolves, if you have an Eevee you are going to evolve, you can force it into one of three evolve forms. That is Vaporeon, Jolteon, and Flareon. They are Water, Electric, and Fire respectively. To do this, you rename your Eevee "Rainer", "Sparky", and "Pyro" also respectively. These guys power up with Eevee candies. Understand this: You can only force evolve into each form ONE TIME. That means you can force evolve into one of each. So, that would be something to consider. It doesn't matter if you have one of the three forms, just one force of each type.
The FASTEST way to gain XP is a very important trick. Totally legit. I don't cheat, not that guy. If you save your evolves and do them a bunch at a time you can get 500 xp per evolve. Now here's the trick. Gather a bunch of them, around 30 to 40, and set off a lucky egg, which doubles your XP for 30 minutes, and do all your evolving in that time frame. This will make each evolve worth 1000 xp. Also, if you happen to evolve into a NEW form that you haven't seen yet, that gives you another 500 XP, doubling to 1000 XP. So, evolving a new form is 2000 XP per evolve. My kids and I call it an Evolve Party. You can get a level or two early in your levels and in the teens you'll certainly gain a level until your late teens. It takes 30 seconds to evolve and just a little longer if it is a new one, so you can theoretically get 60 evolves in a single egg... but that ain't actually happening, trust me.
The best to evolve are Pidgey, Weedle, and Caterpie all only require 12 candies to evolve. Each catch gives you 3 candies plus the pokemon, if you turn it in to the professor you get another, so every 3 catches of these guys is an evolve.
Final evolve part tip is, set up which ones you want to evolve, and star them so they are on top of you list, if you sort by star, so that you don't have to dig for them wasting precious time.