Don't tell anyone about our plan.

Literal

We [of-の] plan [object-を] anyone [to-には] don't-speak [emphasis-よ].

誰にも ('to anyone, not to anyone') — indefinite 誰 + に (to) + も (also/even) + negative verb = 'not to anyone at all.' しゃべる is a casual verb for 'to talk, to chatter' — more informal than 話す. A conspiratorial warning to keep a secret.