As a resident at a Central Initial Reception Centre (ZEA), you will also be given a HVV travel ticket for all public transport in Hamburg. A few days after your arrival, the social management team at your accommodation will give you this ticket. The ticket must be returned as soon as you move to secondary housing or receive official refugee status and receive all future benefits from the Jobcenter. You should then ask for a Sozialkarte (social services ticket) which entitles you to a discount on a monthly HVV ticket.
When you move from your initial accommodation to subsequent housing, you need to buy your tickets from the HVV. You can buy tickets from the bus driver in a bus, from a ticket machine or at one of the HVV service points.
You do not need to validate your ticket. When travelling by bus you should enter at the front of the bus and show the bus driver your ticket. Ticket inspectors will check your ticket on the U or S Bahn. For this reason, you should always keep your ticket until after you have left the station!