That's self explanatory, I think...How did you discover Star Trek?
For me, it was a TOS episode...The Tholian Web...And then my stepfather recorded Wrath of Khan off the TV...I think it was 1986-ish...And then of course, TNG premiered a year later. I was 8 (in '86).
The late 1970s. It was rerun continually on British TV - or rather, it was the only series which was rerun regularly on British TV - and I HATED IT.
The reason was that it was used as a summer replacement for British shows I loved, so the BBC announcers would say things like, 'And that's the last in the current series of Blake's 7, but next week, by popular demand, another chance to see classic science fiction as the crew of the Starship Enterprise go in search of Spock's Brain'. Why not rerun Blake, or Doctor Who, I'd think, rather than the fifth chance to see Star Trek? Particularly if the Trek repeat opened with a stinker... It wasn't that I really disliked Trek, but getting a fourth chance to see even good episodes, when there were episodes of Who and Blake I'd only seen once (or never), didn't excite me.
In later years, I found out the background - that agreements with the writers and actors unions limited the number of British shows could be rerun each year, whereas American shows could just be bought in. And Trek was the one that stayed popular how many times they ran it, so...
When did I start liking Trek? 1983. Finished my book, half hour wait til the bus home from school; there's Vonda McIntyre's novelisation of Wrath of Khan in the library... got it, started it, loved it, decided to give the series another try.
Addition: I'd half forgotten this, but my very first memory of it is seeing Yesteryear (TOS) in the mid-1970s and loving it (brainy but bullied kid wins out - perfect for me), and later being astonished to find they'd made a live action version of it, even if I didn't like it nearly as much as Doctor Who...