I'm just a little confused. I just want to make sure I watch everything in the correct order and such. Why does the website Anime Planet say that there are only 13 episodes of Natsume's book of friends, when CrunchyRoll has 39 episodes?
Natsume is divided up into 4 seasons. You can see the rest of them at the bottom of the anime-planet page:
It's similar with Anime News Network.
But Crunchyroll has them grouped together under one listing (but for some shows, the different seasons are listed within the show's page). They do that with a lot of multi-season shows, perhaps in an effort to make the favorites/queues work easier so you don't have to hunt down different listings for different seasons of the same show.