Those of you playing Pokémon GO are probably sick to death of seeing the same crappy monsters no matter where you go. Pokémon GO doesn't tell you this, but even those shitty critters can still be mega useful. Pokémon encounters are somewhat tied to location, yes, but they also take into account your level. The higher level you are, the more likely you are to find rarer and more powerful Pokémon. The easiest way to level is of course to keep playing, but in particular you want to keep capturing everything you come across. Yes, even that 10 CP Pidgey.
The thing is, you get XP for evolving Pokémon. And lower tier Pokémon have small evolution requirements: A Caterpie for example only needs 12 Caterpie candy to become a Metapod:
You may already have a Metapod, or a Butterfree, but taking the time to evolve a Caterpie in this example still nets you at least 500 XP (as does any other Pokémon evolution). Each and every Pokémon you capture nets you 100 XP too, regardless of how powerful that creature is. Over time, your XP gain from terrible Pokemon does add up.
(If you're lost, you gain candy by "transferring" Pokemon to the professor. To do that, tap on a monster and scroll all the way down to find the transfer button. One Pokemon transfer = one candy of that type.)
If you want to power grind, you need to time your evolutions right as well. As you already know, a Lucky Egg gives you double XP for 30 minutes, so one evolution becomes worth 1k XP. A good idea is to evolve all your weak unwanted Pokémon in one go, for maximum gain.
Eventually, all those trashcan Doduos that plague your streets will pave the way for much cooler Pokémon, so make sure to keep capturing them.