Mark me; literally, look to me; i.e. "attend to me," for I am about to say something well worth attention. And be astonished. Prepare yourselves, i.e; for something that will astonish you. And lay your hand upon your mouth.
Harpocrates, the Egyptian god of silence, was often represented with his finger on his lips. The symbolism is almost universal. Job begs his auditors to "refrain their lips," and, however much astonished, to keep silence until he has concluded.