You can start from the chapter where the anime ends. Usually, there are forums or fan communities that can give you precise details on which chapter to pick up.
It's a bit tricky to pinpoint exactly where the Noragami anime ends in the manga. But generally, it leaves off before some of the later arcs in the manga.
The Noragami anime is reasonably true to the manga. There are a few alterations made for the sake of animation or to streamline the story, but they don't significantly deviate from the manga's main themes and events.
The Noragami anime is a relatively faithful adaptation. There are a few tweaks here and there for better animation presentation, but the core story remains intact.