Having the AR camera on (the one that uses your rear camera whenever you are trying to catch a Pokémon) is a fun novelty, but it makes it FAR tougher to catch Pokémon. When you turn off the AR camera, the stock animated background will appear, and the Pokémon will be stuck in the center of it, never moving no matter what you do. This makes them EXTREMELY easy to catch. This also saves battery life.
If you have one of your Pokémon stationed at a gym, you can earn experience points by training at your own gym. This will allow you to gain experience points without the risk of having any of your Pokémon faint. Doing this method will also allow you to earn gym prestige.
At any other gym, you can sometimes earn experience points even if you only beat the first Pokémon stationed at the gym. Test the waters by beating the first one and running away, then seeing what you get. If you get experience, then go back there and battle again, as many times as you want to so that you can load up on experience points. This is especially effective if you hold an elemental advantage against the first Pokémon at a gym.
Eggs can be hatched based on either the speed that you are moving at or the pedometer on your phone. The common thread is that the game has to be active. If you go too fast – more than 12 MPH – the speed stops counting, but if you are riding your bike at 9 or 10 MPH it still counts the distance based on the GPS. If you are running on a treadmill, the distance is counted based on the pedometer so even if you are not moving in your GPS map, you are gaining distance for the egg.
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Interestingly, moving on a treadmill causes Pokémon to appear, despite not moving on your GPS at all. Of course, you have to be holding your phone and moving it as you run, not sitting it on the stand or holding it still. But hit the treadmill for awhile, or run in place in a similar fashion, and your phone will sense movement, and Pokémon will start appearing despite not having used any incense.
You get 500 experience when you hatch an egg and 500 experience when you evolve a Pokémon, so evolution and level-ups are your key to gaining a ton of experience. The cheapest/easiest to evolve are Pidgey, Rattata, Caterpie and Weedle so load up on their candy and mass-evolve them for a ton of experience. Use a Lucky Egg before you do this so that you can gain 2x the experience during the whole thing.