Evolution is weird. The only Final Evo I have found in the wild is a Pidgeot, but that asshat was too hard to catch.
The normal way to evolve is by catching a bunch of the same type of pokemon. There is a feature called transfer in which you transfer a pokemon to the professor permanently, and the professor gives you a candy.
Ex If you transfer a charmander, you get a charmander candy etc
When you catch a pokemon you get a candy as well. The candy is used for two things, power up and evolve. I have only evolved three pokemon so far, the Raticate, Magneton and Caterpie. They both had about a 15 candy evolve requirement. So you need a certain amount of candies to evolve.
The Caterpie only cost 5 candies to evolve to metapod. From metapod to butterfree it cost 12 candies. Some of the rarer pokemon cost more candies to evolve.
Ex my Ryhorn cost 20 candies to evolve, and so far I've only come across one. Growlith cost 20 as well.
Powering up uses candies, but only 1 or 2 (that I have found so far) but it also uses another currency called stardust which you get from catching any pokemon