For me it was 17-18 in the pub. Wasn’t discussed at home, well at least not “in front of the kids”, so it was overheard conversations by the grown ups giving each other stick over Labour this and Tories that, and then later at work.
Somewhere between the 1970 election and the first in 74. Politics and current affairs were to the fore at home. Both parents avidly consumed newspapers and TV watching had to fit in with mostly BBC News at 6 O'clock and again at 9. As a reward for passing the 11 plus I was given a Sinclair Micromatic radio and listening to Radio 4 from bedtime at 08:30 until closedown became a habit.
Initially the nice Mr Heath and the sympathetic write ups he got in the Yorkshire Post convinced me but The Guardian, of which my Dad was a devotee, became a more convincing organ.
19 - a mate of mine got me a volunteering gig as a steward at music festivals like Reading and the Phoenix festival. It was through the student wing of the Labour Party. The organised coach back to London was full, so they asked for some volunteer men to give up their places. My mate and I jumped off and hitched our way back in a decommissioned ambulance full of hippies and copious amounts of weed. I started the week a tory light, got swayed by John Smith’s legacy and the rise of Blair and ended up a very relaxed communist.
I was a well brought up Tory until I went to University (1992-1995) and met other people who were not (the benefit of Private Schooling is that they can set your politics up for you). One of my friends was a staunch Tory and it became apparent that he was a bit of a tit. My other best friends were much more politically diverse - one has a great skill at paying devils advocate to try and make you really think about what it is that you are arguing.
Plus I started to read Private Eye and quickly discovered just how venal and corrupt many politicians are. This has made me very centerist in my old age.