Last year, approximately 160 candidates were invited for a visit and 95 candidates were interviewed. The committee recommended that 32 full scholarships and 60 partial scholarships be offered. There are three scholar's visits per year, the first being in November, and the other two in January and March.
As for the trip, its more or less like any other pre-knob visit, except that everyone on it is competing for the scholarship. You'll arrive on a Thursday afternoon, and go to a number of meetings and attend dinner with the knob you'll be shadowing. You'll then have a meeting with ROTC representatives, and then go back to your respective barracks, where you'll have time to ask your knob and their roommate questions. In the morning, you'll attend sweep detail, breakfast, morning classes, and lunch. On Friday afternoon you'll discuss your essay with a professor and a few other candidates. The scholarship committee will consider the comments of that professor, your admissions information, and the comments of Dr. Rhodes, if you chose to interview for the Honors Program while you visited.
I would highly recommend the Honors Program. It really helps give you that edge, academically while at The Citadel and professionally after graduation.