Vserian,
The Residence/Work Visa takes about a week from the day they take the passports to DNRD for processing.
Normally you will arrive in Dubai, be placed in accommodation, and left alone for a few days to acclimatise to Dubai. On the first or second formal day of work (Induction), your passport will be sent for visa "stamping". You will be advised via email when to collect it. I seem to recall that mine took 3 working days to process.
I hope that answers your question.