It doesn't matter how high your level is, scoring Great Throw and Curveball bonuses add up quickly.You can actually start throwing a Poké Ball as soon as you see the Pokémon on your screen, which is a big deal. The Pokémon is not only closer to you, but the capture ring is usually fully open. Start flicking up on your screen as soon as you see a Pokémon, and that Poké Ball will almost always hit its target and capture the Pokémon before it has time to struggle or flee.
If you find yourself unable to hit a Pokémon because the ball keeps sparkling and flying off to the left or right, you know the only way to reliably hit that Pokémon is with a curveball. So get good at it!
Every Pokémon has a type. That type has a natural strength, a natural weakness, and in some situations a type that completely nullifies attack and defense. You don't want to head to a gym only to have it end in a stalemate, nor do you want to get crushed by something a much lower level than you because you weren't paying attention.
Look at the Pokémon protecting a Gym before you attack. Look for their type, and make sure you have Pokémon in your starting six that will do as much damage as possible to that type. When leaving multiple Pokémon as a team, make sure your team isn't leaving a lot of the same type to guard the gym. Here's a quick list of the elements and their natural opponents.
Hatching Eggs in Pokémon Go is all about traveling a specific distance. You have to travel 2, 5, or 10km in order to hatch an egg, and when you do so there's a Pokémon and a boatload of Pokémon candy inside. Even if you get a weak Pokémon in an egg, the candy gets you much closer to evolving any of that kind later on so make sure you are hatching as many as possible!
The game wants you to walk the above distances with the app open on your phone, which is awesome. It means people are getting out there and doing more wandering about than ever before. It also means they're doing it the hard way. Pokémon Go accepts any movement under 6.5mph as distance traveled in hatching an egg. That means you can use a skateboard, a bike, or even a driver in a sufficiently large parking lot to quickly hatch those eggs.
Keep it under 6.5mph, but be sure to be safe about it, and everything is awesome.
Don't let yourself get lured into this trap where you can only play with members of your own team. "It's a slow you down move", and will actually slow down your leveling process. Ideally, you want to travel with at least one of each faction, and that way you can all take turns setting up and taking down gyms, as you cycle through that process, everyone will level up quickly and become more capable of playing solo.
It also means when you finally do travel with only the same team as yours, everyone on your team is better equipped to leave a wide variety of Pokémon at a gym. Variety and diversity are important in this game!
When you get enough Eevee candy to evolve one, the results are usually randomly split between Jolteon, Flareon, and Vaporeon. No matter what kind of Eevee you get, or what special attack or size you capture, the results are random.
HOWEVER.
If you absolutely must have a specific Eevolution, there's a one-time Easter Egg that will control what you get. In the television series, there's a group of players called the Eevee Brothers who each had one of the evolved Eevee elements. If you name your Eevee after those characters before evolving it, the Eevee will become whatever you name it.
This is only guaranteed to work once for each of the Eevolutions, so pick your Eevee carefully.