When and how were animal tithes given?
A general principle about tithes is that each year’s “crops” must be tithed separately. This is true for the animal tithe, just as it is for agricultural tithes. Thus there must be a date on which the year changes, and this should be at a time of year that provides a clear separation between the old year and the new year, i.e. a time when there a very few borderline cases. Since farm animals generally give birth in the spring, the best time for the year to change for animal tithe purposes is in the fall. There are two opinions in the Mishnah about the exact date of the change. According to R.Meir it’s the first of Ellul; according to R.Eleazar and R.Shimon it’s the first of Tishrei (Mishnah Rosh Ha-Shanah 1:1 and Bechoros 9:5-6).
The animals born in each year were tithed, i.e. a tenth of them were brought to the Temple as sacrifices. The process of selecting this tenth is briefly metioned in Lev.27:32, and is described in greater detail in Mishnah Bechoros 9:7-8.