Using it on the day when it becomes usable: Yuma 62b
Considering the animal to be eligible from the time when it is one day into its year, as though it had completed its year: Rosh HaShanah 10a-b
Specific Animals
For a calf: Rosh HaShanah 10a
For a bull: Rosh HaShanah 10a
For cattle: Rosh HaShanah 10a