They would place their palms facing upwards when praising a celastial deity, down when praising an Underworld deity. They would visit temples and pray, and priests and priests were appointed for the Gods. They would also animal sacrifices and large fires, and they would often carve small woodcarvings and leave them in temples for deities. Then would also stand around a temple and do a little rain dance to prey to the gods or entertain the gods for a good rain season to grow heir crops.---- Many Ancient Greeks were members of cults (simply a sect or denomination in worship of a particular deity/deities). For example, the Eleusinian Mysteries were only taught to initiates, so their practises are no longer known to us as persecution of Pagans became rampant and temples and holy places were desecrated.
Daily, public worship, however, was adapted by the Roman Empire.
See http://en.wikipedia.org/wiki/Religion_in_Ancient_Greece#Practices for more detail.