I did a couple of these when I was in the Livejournal wilderness, at http://justaddfur.livejournal.com/ Now I'm back "home", I'll answer it here :)
How did you come across your favorite author(s)? Hmmm .... this varies. Some I just happen to pick up if the book sounds interesting and quirky (Marian Keyes) some were introduced to me (Tolkien) and some evolved unexpectedly out of my modernist fiction paper at university, 100 years ago (Gabriel Garcia Marquez, Grahame Greene)
Recommended by a friend? Probably some. I'm a recent _ and complete _ Discworld convert; and they were recommended by my husband. And when I was in high school, more than 100 years ago, my friends and I used to swap books all the time. So I have a nostalgic love of Raymond E Feist, and the early Dragonlance books.
Stumbled across at a bookstore? I stumbled into the Belgariad and the Dragonlance series in bookstores; I came across Margaret Atwood after watching A Handmaiden's Tale.
A book given to you as a gift? I don't get books as gifts very often, which is fine. I"m more likely to get book vouchers, which is also fine. Having said that, one year my mother gave me Tailchaser's Song, by Tad Williams. :)
Was it love at first sight? Sometimes yes. My love for The Lord of the Rings was deep, abiding and instant.
Or did the love affair evolve over a long acquaintance? I'm an impulsive person. My judgement is swift. I either love something instantly, or take against it after a short while. Then I throw it across the room and look for something else to read.