Athens Urban Transport Organisation runs the city buses, which run frequently and cover a great deal of the city. There is no comprehensive bus map, however; for routes, you must call the info line, check the website (click 'OASA Telematics') or, the best option, use Google Maps' directions feature, which integrates metro schedules too.
The unified Ath.ena Ticket, a reloadable paper card, is used across the transit system. It's available from offices and ticket machines in the metro. Single rides cost €1.40 (good for 90 minutes); a 24-hour/five-day travel pass is €4.50/9. A three-day tourist ticket (€22) can be purchased at the airport and includes round-trip metro to the city. Children under six travel free; people under 18 or over 65 pay half-fare. Swipe the card at metro turnstiles or, on buses and trams, validate the ticket in the machine as you board, and keep it with you in case of spot-checks.
If you're staying a while, you may want the sturdier plastic Ath.ena Card, which may be purchased at most metro ticket offices; you must load at least €4.50 to start.