Determining the birth date of an ancestor can range from super-easy to extremely tricky.
Some sources to check:
(1) Birth records - obviously!
(2) Cemetery records: Hopefully, the gravestones or cemetery records will have the full DOB, or at least the birth year. In some cases, the date of death will be followed by the age at death. [67 yrs 2 mo 14 days] This requires a little math!
(3) Death certificates/records
(4) Newspaper obits, death or funeral notices
(5) Probate files: The ages of minor children may be included, or at least recognition that they are minors.
(6) Marriage records: ages may be included; if bride or groom is underage, then a family member will grant permission. Know the ages that people customarily marry at a given time in history. If males generally married between 20-25 and women between 18-22, then you have a workable range.
(7) Census records: don't depend on ages being accurate. Sometime people fib, or the informant may be wrong.
Try to find multiple sources for births. I have cases where the age on death certificates is wrong and the census is right!