Most men whose careers look like Wentworth's started at about twelve or even younger. Getting started was about getting a captain to take you on as a 'Boy 1st Class or Volunteer' on his ship. As you went on you would be rated as 'midhshipman' and then take the exam for lieutenant. Surprisingly perhaps this was how the officer class were principally recruited, by individal captains. In theory, captains were then responsible for the education of their 'young gentlemen' - hence Wentworth, who clearly took this seriously, being only two perticular about the schoolmaster, ie he made sure the boys applied themselves (and probably also made them write decent letters home!). There was a Naval Academy, at Portsmouth, which was in fact where both the Austen brothers started their careers, but it was a minority who entered the service through this central route. Here is an old L&T post of mine with a bit more on naval careers.