"digame" and "vamonos"
Not sure of the spelling, I think it means give it to me, and go away?
Digame = Tell me or speak to me Vamonos = if it is used as "vamonos digame" then translates as "come on tell me!" or "come on speak to me!" in a more formal setting.
It can also be expressed as "vamos, cuentame" or "vamos, dime" in a more familiar setting.
In reality the word "vamonos" is made up of two words and means we go but in this case it is used as encouragement for someone to perform an action.
Vamos = Verb -- To go nos = abreviation for nostros = we
dígame = "tell me!" (sometimes it uses this when answering the phone)
vámanos = "let's go!"
According to 501 Verbs, "vámonos" is the first person plural imperative form of the verb "irse" (to go away) and, as others have said, it means "let's go".
"Give it to me" would be "Dámelo." (Or Démelo... to "Ud".) And "Go away" would be "Vete". (Or Váyase... to "Ud.")