Lonnnng time ago
John Peel, New Musical Express and Melody Maker
Sometimes the support band was good EG. Greatest Show on Earth supported Tony Williams Lifetime
Festivals had bands we didn't know

I discovered a heck of a lot of my more recent music from reading Uncut Magazine, and I've taken up an annual subscription again this year after a break of 5 years or so.  Listening to other people's choices here and at TAS has brough new (to me) acts into my musical world too.

When I was younger it was mostly obligatory NME (the ENEMY as my dad used to pronounce it), Sounds, and Melody Maker.

In between times, I bought stuff like Zig Zag and Time Out after I started working in London. I also formed a friendship with Geoff (a.k.a "Clip") the guy who was running James Asman's Records, on Cannon Street. He took over from Dave Ruffy, who formed The Ruts, and who used to pop in for a chat every once in a while. That's how I got into a lot of punk, as well as other stuff that was described as punk, (even when it wasn't, e.g. The Stranglers) as well as British reggae bands like Misty In Roots, and the whole Rock Against Racism movement.  Geoff went on to form a band named Orior, and they gave me my first and last record sleeve credit, for building their guitarist's fuzz box. 

I was also a semi-serious collector in those days, so Clip would give me first dibs on any interesting-looking picture discs, or coloured vinyl releases. Some of them I even played.

For a time I had a girlfriend/fiancée who ran the record department of a local electrical store, so I used to get a lot of new-artist promos that way.  That was how I discovered John Otway.

Lastly, as John mentioned, records from charity shops, before they had people who checked how much stuff was worth, damn them. At 20p-or-whatever a pop, one could afford to take a chance or three.