I either carry around a little notebook or use the notepad featue on my cell phone to jot down ideas. Story ideas are far and few between now, simply because I've recognized what good ideas look like. If one sparks my interest, I'll mull it over and over around in my mind until I've got the formation of a decent story. At this point, I'll devote a notebook page and scratch out a few ideas. One may call this outlining. I do not. For me, just getting it down on paper helps to release my conscious mind from holding onto it, making room for new ideas.
Before college, the thought of writing short stories never entered my mind. I wrote novels, even in high school. Then, when I read a biography of Stephen King and knew he started out with short stories, I allowed myself to find ideas that fit within the short story structure . . . and the floodgates opened widely, just like the tidal wave of blood in The Shining.
During this time, I worked for my uncle Rod, who's a contractor. Many times, the jobs he had required me to travel at least 20-30 minutes out into the country. I loved these times, and almost every single day, I'd come up with a new story idea. 95% of them were crap, when I look back on them now (oh, who am I kidding, it's probably 98-99%) but I was getting myself used to the idea of generating story ideas.
Late last year, I had two short story ideas that just wouldn't go away, no matter how much I was working on something else. Both were along the fringes of science fiction, which is odd because most of my ideas were horror, fantasy, or thrillers. One of these days, I'll post them for you. I like them, and they were fun to write.
To me, I love the entire writing process, from idea generation to writing first drafts to editing. But I think my absolute favorite is getting the ideas and churning them over and over as if I were churning milk into creamy butter.