My current horse I found on the internet (back in 2002). He was a young foal located all the way accross the continent and after searching for about a year and getting VHS's of one ordinary foal after another, I ordered a tape from a warmblood breeder in New England. There were lots of fantastic foals on there. They were double my price range but I then realized if I wanted what I really wanted I would have to pay for it. One foal jumped out at me on that tape and a few days later I was on a plane to see him in the flesh. After he was weaned, they shipped him out and he is now 8 and we are loving life together.
My very first horse was an off the track TB mare that my riding instrutor at the time had aquired. She was so beautiful, but only 3, and quite reactive and marish. After having her a while my instructor would let some more the the advanced students ride her, and then I got to ride her. I ended up leasing her for several months and then she went up for sale, so naturally I did what any other 13 year old girl would do. I begged my parents to buy me the horse and they did!
My second horse was another one that I found word of mouth when I was switching trainers. I wanted to do Young Riders in dressage, so was pointed to a trainer known for developing young riders. I told her I was looking for a horse and she had a YR school master for sale. I tried the horse and it was love at first sight.
So basically, before the internet was around, I found my horses through word of mouth. Now that the internet is here, I do all my horse hunting online. Now and then I will browse a magazine, but not too often.