Whenever I get a story idea, I type it up in a Word document and save it. Sometimes I'll go ahead and outline, develop characters, research, and make notes for when I'm ready to write it. Other times it just sits there as a vague idea until I'm ready to take it further. If it's an idea I can't get out of my head, I might go ahead and play around with writing a beginning, but I only post the ones I can't stop writing. I try not to have too many unfinished projects online at once, although I've been really bad at following that rule the last couple of years.
I don't have any special process for getting ideas. The best ones are the ones that just strike like lightning, out of nowhere. But when I don't have those inspired moments, I've succeeded in forcing ideas by deciding on a genre or type of story I want to write and just thinking on it until I can pull an idea together. Secrets of the Heart and Guilty Roads were both conceived that way, whereas Curtain Call was the inspired lightning strike. I tend to have better luck writing the lightning strike ideas because they don't feel so forced and contrived.