A thanksgiving offering is mentioned in Leviticus 7:11-15 (NJPS):
This is the ritual of the sacrifice of well-being that one may offer to the Lord:
If he offers it for thanksgiving, he shall offer together with the sacrifice of thanksgiving unleavened cakes with oil mixed in, unleavened wafers spread with oil, and cakes of choice flour with oil mixed in, well soaked. This offering, with cakes of leavened bread added, he shall offer along with his thanksgiving sacrifice of well-being. Out of this he shall offer one of each kind as a gift to the Lord; it shall go to the priest who dashes the blood of the offering of well-being. And the flesh of his thanksgiving sacrifice of well-being shall be eaten on the day that it is offered; none of it shall be set aside until morning.
I have a hard time understanding what was involved here. Under what circumstances should the sacrifice be made? Is it up to the person making the sacrifice to do it or not? Does this passage require three different types of cake? If so, what's the difference between them? What sort of animal is involved in the sacrifice? Who eats the flesh of the sacrifice: the priests or the one who provides the sacrifice?
Wikipedia is remarkably terse about the ritual, but suggests that:
In Psalm 107:22 and elsewhere no physical offering, only praise, is implied.
That seems at odds with Leviticus 7.