Greetings to you!
From what my research has gleaned (very sparsely sourced), the Greeks had massive public festivals and rituals to Athena. Most of course at the Parthenon. As to individual practices, very few references survive, but most point to libations, prayers,hymns and offerings. The libations were: mixed wine/ water (red, perhaps?),un-mixed wine, honey,olive oil, water or milk. Prayer was offered with arms upward,or the right arm out to hold a'phial'(shallow bowl for this purpose). The wine was poured from a container into the phial, then the 1st cup poured following was drank by the offerer. offerings given to the main altar or the personal altar were: cereals (grains), fruits/ vegetables, honey, water/ wine and flowers. As to hymns, there is an excellent article with audio in Wikipedia as to many of the hymns and paens voiced by Greeks. It seems to be a great place to start, and may her wisdom guide you.