on arrival, follow signs to S-Bahn/DB, buy ticket(s) from machine,you need cash for that. depending on group size and If all want to go together all the time. (f.e. if 8 in group- can split between 3-5 or 4-4 or 2-3-3).
The normal tickets are valid from 9.00, mo-fr, till 3.00 next day (incl nite buses) on ALL local transport, train, incl S-bahn, U-bahn=metro, bus, some cross harbour ferries untill city-boundaries. Main exception are the sectors In Hamburg city for long distance trains (ICE etc.).
You can upgrade the daytickets for use 1st cl and ''schnellbus== express bus (runs to some outer areas not well covered by rail), for the average tourist thats not needed. You can also buy more expensive tickets to cover larger areas, out of town. All are for 1 or 5 persons.
IN the HBF are 2 info-offices, dispensing maps and general info etc.
There is also the HAMBURG Ticket/pass, for sale from tourist info, that includes this daytikcet (basic) and entry or discount to some tourist attractions.