Other than temples, your main way of petitioning the gods for their aid is sacrifice. You can sacrifice from the Magic Screen, or do it during events.
While seven cows (or cows worth of goods) is a standard sacrifice, it is not a generous one; if you're worried about your sacrifice being enough, twice as much is better.
Sacrificing to a particular god is likelier to work if you have a worshipper of that god on the Clan Circle. Devoting Clan Magic to Ritual at Sacred Time also helps.
Emergency sacrifices during events can also go better if, at Sacred Time, you devoted magic to the relevant god's sphere of influence. Fields magic makes it easier to call on Nyalda and the other earth goddesses, Health magic helps your priestesses reach Erissa, War magic helps you call on Elmal and Osara, and Wilds magic makes it easier to reach Dostal and Inilla.
Most gods don't care whether you sacrifice herds or goods to them; they value both equally. Exceptions include the gentle healing goddesses Erissa and Chalana Arroy, who dislike bloodshed and may not react well to sacrifices of cows, and Humakt, who, as the god of death, prefers animal sacrifices. And of course, herds produce more herds and goods do not, so it's usually best to sacrifice goods if you have a choice.