My first book was Mistborn after which I completed the trilogy. I honestly don't remember how I found it, but I've always loved fantasy so its possible I just stumbled across it while perusing the fantasy section of the local library. Although I did like the trilogy, at that point I was not specifically a Sanderson fan. It was just a series I liked, and it was only later, which was about 6 or 7 years ago now, that I actually became a fan. My roommate at the time had The Way of Kings and he had suggested it because I liked fantasy. I read it and loved it. Words of Radiance had just come out and I quickly mowed through that as well. At that point I had connected Brandon Sanderson with awesome fantasy books and moved to Warbreaker and Elantris which my roommate also owned. I then researched Sanderson's books and realized that Mistborn, which I had read already, was also his. I reread them which was when I started to make the realization that there as some sort of connection between some of his books. Ever since then I've been reading all the Sanderson cosmere stuff I can get my hands on, plus most of his other series.
So basically I owe my obsession with the Cosmere to my roommate.