Learn French: Surtout, ne dis rien ! - Above all, say nothing!

In French, the negative word rien (nothing) replaces pas. The structure is ne ... rien (not ... anything / nothing). Saying ne dis pas rien would be incorrect, much like a double negative in English!

Why does the command dis end in an "s"? I thought the "s" was dropped for commands.

You only drop the final "s" in the tu (informal "you") command form for verbs that end in -er (like parle ! or mange !). Because dire (to say) is an -re verb, it keeps its normal "s" ending in the command form: dis !.

Does surtout literally translate to "on all"?

Yes! It is a combination of sur (on/over) and tout (all/everything). When joined together, surtout is used to mean "above all" or "especially."