Ais was born 1000 years ago. She lived in that era for the first six years of her life, with her parents, potential other relatives, and her parents' friends, until the Black Dragon descended on her home and killed everyone, though her dad managed to put out its eye. Somehow, during that, she was thrown forward in time. The exact means is still uncertain, but she was either sent forward by some sort of portal, or magically frozen. In either case, she arrived in the modern era at the same age she left the ancient days in; six. She then spent the next ten years in Loki Familia as an adventurer.

She is sixteen years old.

What Rabid said is accurate except that she was seven, not six. So, she has been an adventurer with Loki familia for about 9 years now. Also, Aria is likely alive since Ais's goal is to "take her back". We don't know what state she is in though. It is a common theory that the dragon absorbed her and her power somehow which is why the dragon is so strong and why Ais will likely be key in defeating it.

I have always understood that she was six when she was sent forward, and turned seven within the first few months of being an adventurer.

She was seven when she registered in the Guild, which she did the same day she got her falna.