Arguably, the word говно (govno) should be translated as "crap", rather than "shit" -- i.e., it's rather vulgar, but it's not quite as dirty as the "S-word" is in English. But in any case, as the Russian slang dictionary explains, it's generally used in literal reference to "fecal matter", or metaphorically to say that something is as worthless and disgusting as "the brown stuff". However, it's seldom or never used as an Obscene Interjection, the way we say "Oh, shit!" in English.

The word чёрт (chyort) literally means "devil," and it's used roughly the way we use "hell" in English. So in contexts where English speakers would say "What the hell?" or "Go to hell!", Russians say Что за чёрт? ("What the devil?") and Иди к чёрту! ("Go to the devil!") One can also just say Чёрт! as an interjection to express surprise, anger, dismay, etc. -- in this context it's functionally similar to "Oh, shit!" (but a lot milder).