"I got top marks in Concealment and Disguise during Auror training without any study at all, it was great. I only qualified a year ago. Nearly failed on Stealth and Tracking. I'm dead clumsy, did you hear me break that plate when we arrived downstairs?"
-- Nymphadora Tonks (OP3)
Tonks completes her three years of training and qualifies as an Auror. As a Metamorphmagus, she excelled at Concealment and Disguise training, but she noted that her natural clumsiness made Stealth difficult (OP3).
In August of 1995, Tonks tells Harry that she only qualified a year ago, which would be 1994. Auror training takes three years after seven years at Hogwarts, so we can extrapolate back to determine her birth year.
The path to becoming an Auror is not an easy one. McGonagall warns Harry of this when he expresses his desire to become an Auror:
"You'd need top grades for that," said Professor McGonagall, extracting a small, dark leaflet from under the mass on her desk and opening it. "They ask for a minimum of five NEWTs, and nothing under 'Exceeds Expectations' grade, I see. Then you would be required to undergo a stringent series of character and aptitude tests at the Auror office. It's a difficult career path, Potter, they only take the best. In fact, I don't think anybody has been taken on in the last three years." (OP29)
If true, it would mean that Tonks was the most recent Auror recruit when she meets Harry.
McGonagall goes on to describe the requirements:
"Well, you'll need to demonstrate the ability to react well to pressure and so forth," said Professor McGonagall, "perseverance and dedication, because Auror training takes a further three years, not to mention very high skills in practical Defence. It will mean a lot more study even after you've left school, so unless you're prepared to -"
Tonks is a very talented person indeed, despite her lack of the ability to "behave herself," as she put it.