For me, I do a general character outline on notebook paper. Name, age, profession, family. A few personal things. Just enough to give me an idea about who the character is. My characters develop as the story develops, and I just love the surprises! In my historical romance, To Save a Lady, I had no idea Elise was a window-shopper. It was just something she did on her own and I knew it was an aspect of her character that had emerged during a scene.
Besides little surprises, there are big ones. Darlene, my Southern Lucille Ball/Marilyn Monroe gal, is one of my most popular characters and one of the most fun characters I've written. She was totally not planned. Years ago, I was planning to write a story for a contest and it was going to feature two dimwitted crooks. In that story, a blonde came running out of the house where they were stealing gasoline out of the mayor's Cadillac. I just called her Darlene because that sounded like the 50's. I never could make the story work and a couple of years later, I was thinking about it and it hit me that it was actually Darlene's story. Once I went with that, the story came together and so did Darlene's character. I just started out with her wanting to be a movie star like Marilyn Monroe. Her enterprising attitude all came about when I put her into action in the story.
Another big surprise was the character, Rafe, in To Save a Lady. I was writing a scene with the hero, Jesse, on Grand Terre island. And up walked this guy and I was like who are you? It turned out he was Jesse's former roommate at school, the son of an admiral and now a privateer. He actually played an important role in the conclusion of the book. Although the second book was supposed to be another character's story, I knew the second book would be Rafe's.
For me, the surprises like Darlene and Rafe are what makes telling a story surprising and fun for me.