“Nothing” means “ничто” (nichto) or “ничего” (nichego) in Russian. It means “not a single thing”. You can use this word when you mean something unimportant. “Nichego” is the negative pronoun “nichto” in the genitive case. If someone asks you, “What have you eaten today?” (“Chto ty segodnya el?”), you can reply, “Nothing.” (Nichego”).
“I said nothing” is “Ya nichego ne govoril” in Russian. “Nichto” is a pronoun-noun in negative sentences. It means “not anything; no single thing”. You can use it in such sentences as “This means nothing to me” (“Dlya menya eto nichto.”).