if the refugee lives in a camp inside Berlin he can grab his arrival papers and go to the lageso and get a ticket from bvg workers who will be there.
The ticket will be granted within the first 3 month after arrival.
The monthly payment will be reduced by 26€ so the ticket is not entirely free of charge.
If he lives in a flat, he needs to bring his arrival papers to the burgeramt. There he will get a Bewilligungskarte. With the Bewilligungskarte he can buy a public transport ticket with a discount. It is called Wertabschnitt and the price depends on the reach.