How exactly does the Careers' system work?

This is how I initially thought it worked:
The potential Careers train throughout their childhoods, then every tahun the best male and female candidates are selected. There's a Reaping which is purely ceremonial. Whichever names are actually selected, the chosen candidates volunteer.

However, I'd have thought that every tahun (or almost every year) those candidates would be 18. It'd make sense. They'd have the most training years they can, they'd be bigger and stronger.

But Finnick was 14 when he was in the Games, and I've heard that Clove was 16. So how does it work?