You can pick up a taxi in Athens and other big towns even when there's already someone in it – all that matters is that you are going in (vaguely) the same direction. Stand as near to the road as you dare (in spite of the apparently terrifying nature of the traffic, it's very unusual for people to get run over) and extend your arm – you may call "Taxi" if it makes you feel better. When one eventually slows down, yell your approximate destination (not the address) at the driver. Usual practice is to ask either for the district (e.g. Kolonaki) or the street (e.g. Stadiou) If he throws open the door and yells "Kathisate!" (literally "Sit down") then get in. Everyone pays their portion of the fare, which keeps the prices down. Alternatively, if you are in Athens there's the new Metro, which is efficient, clean, cheap and goes everywhere that you're likely to need, but is a lot less fun.
Public transport is frequent, cheap, crowded – buy your tickets from a periptero (kiosk) or the small office you'll find at the main bus stops. You cannot buy a ticket once you're on board. Routes are usually easy to work out with the aid of a good map, the main exception being the trolleybus service in Athens which is highly esoteric – but if you do figure out a route, stick with it as trolleybuses are less prone to traffic jams.
