Gods and spirits alike require appeasement from mortals.
There are numerous ways of placating the gods: Obedience, prayer and sacrifice . The different priesthoods place different emphasis on these.
Praise the entity, possibly yourself as well. Often prayer involves some sort of request. In such cases it is usually accompanied by sacrifice. Some people consider it boorish to pray for themselves, and hire experts (i.e. priests, holy men). This also includes commisioning special rituals at temples.
This involves compliance with the entity's ethos.
Animal sacrifices: Animal sacrifices are considered the most potent, and are cherished by most gods and spirits. The blood is given to the spiritual entity, and the meat to its worshippeers. Some deities favour specific sacrifices: Anu prefers horses, Mithra bulls, Ereshkigal black lambs, Ishum hares or other small, quick animals, Dagon, Nergal and Namtar prefer human sacrifice. Some deities will not accept animal sacrifices (Eos, Hypnos, Kishar)
Sacral Institutions
Metaphysics
Spirits