How old is Hedwig?

It is not stated in canon.

When Hagrid buys her for Harry, she's already an adult, so at least a year old. Maybe older, as she is stated to be a trained post owl.

Snowy owls reach sexual maturity at one year old and typically live to about 10 years old in the wild and up to 28 years in captivity, so that leaves quite a range of possibilities.

As Valorum said in the comments, the owl appearing in the movie is an eight-year-old male (the females have much heavier, almost black barring all over the back and wings).