Until game developers introduce trading, the only other way to collect Pokémon besides catching and evolving them is by hatching Pokémon eggs. You collect Pokémon eggs as rewards for leveling up, and randomly at Pokéstops. Eggs do require a couple things in order to hatch, however.

First, you’ll need an incubator. Trainers will be rewarded with an incubator with unlimited uses early on for leveling up, and you can collect limited-use incubators at Pokéstops. These are usually good for about three uses. Once you’ve got your egg in an incubator, you’ll need to walk. Each egg will have its own distance requirement, ranging from 2km, 5km, and 10km. Once you’ve walked the required distance, the egg will hatch. The longer the distance requirement, the more likely it will be a rarer or stronger Pokémon. However, don’t neglect hatching smaller eggs.

They still yield more experience and candies than if you were to catch the Pokémon. Note that while many Pokemon are hatchable from eggs, only the first level evolution or non-evolving Pokemon will hatch from eggs. Keep in mind you can only hold nine eggs at a time, and any excess eggs you get from Pokéstops will be discarded. Such being the case, keep your eggs incubated and hatch them as quickly and often as you can so not to miss out on any rare Pokémon.

Lucky Eggs
Lucky Eggs are in-game items that you receive after hitting level 9, or you can purchase them in the shop. They double the amount of experience points you collect in a span of 30 minutes.

One trick you can use to level up quicker is to hold onto every type of Pokémon you catch. Then, activate a Lucky Egg and begin evolving your common Pokémon. While doing this, you should also try to activate a Lure Module or Incense to catch as many Pokémon as you can — that also doubles the amount of experience points you get. Fighting a friendly or enemy gym helps, too. Doing all this will maximize the amount of points you can get, and it’s all doubled thanks to the Lucky Egg.