I see there are many more chapters/volumes of Knights of Sidonia than there are episodes. If I were to want to get onto the manga after the anime series finishes, where would I start and are they directly correlated?
According to Manga Updates, the first season of Knights of Sidonia starts at Vol 1, Chap 1 and ends at Vol 6, Chap 26.
It's not actually that easy to answer. The Anime covers most of the source material pretty closely but not all of it. Some events have been left out or altered. Several events have also been shifted around in the time line.
A perfect example of this is the final battle against Benisuzume (Crimson Hawk Moth). It's pretty much the end of Season 2 of the Anime but in the Manga this fight happens in Volume 9.
However, quite a lot of Volume 10 material also made it into the Anime. In the Anime these events, mostly some social interactions and the like, happen before the fight on Lem 9 while they happen afterwards in the Manga. Other stuff has been left out so the Anime doesn't cover all of Volume 10.
In conclusion the Anime (both seasons) roughly cover the first 10 volumes out of 15, with about 5 volumes per season.
For anyone interested in reading the Manga (as a third seasons has still to be announced) I would definitely recommend reading from the start, even if you know the Anime. It's what I did and you can spot the differences and what has been left out or changed in comparison.
According to Manga Updates, the second season of Knights of Sidonia seems to end at Chapter 43.