Usually, I pick up dramas based on my mood. That's why I often alternate from romance to thrillers, etc. Of course, the plot has to grasp my attention in some way too.
Sometimes, I do choose a drama from an actor I'm very fond of, but only if the plot is intriguing. And also, if I really don't know what to watch, I usually start searching for high-rated dramas that seem interesting. I think MDL has a pretty good rating system, so it's pretty easy to find something good.
Oh, and sometimes, when I know what kind of drama I'm looking for, I just search for the recommandations on the forum.