The credit option is the standard. You take the course for a certain number of credits, you get a grade in the course, and your GPA will be weighted based on those two criteria. As far as I know, most (all?) courses required for your major must be taken this way.
Pass/fail is exactly what it sounds like. You take the course and you either pass or you fail based on the professor's expectations. That's usually around the C/C- level. If you pass a course with the pass/fail option, you get credit for the course. If you fail, you do not get credit. The catch is that pass/fail courses do not alter your GPA. So it's good to take a course pass/fail if you want to get credit but you're not confident you can get a grade that will help your GPA. People use pass/fail when they're taking electives that are unfamiliar to them. For example, someone studying political science might decide to take a metal fabrication class. They want the credit but since it's a very unfamiliar subject and they're afraid they might get a B, they would take it pass/fail. You can only have one pass/fail option per semester.
Dropping a course means you un-enroll before the drop deadline, i.e. before there is any penalty for un-enrolling. Many students (typically sophomores and above) have enough flexibility in their schedules that they can over-enroll, i.e. sign up for a ton of courses, go to all of them for the first week or two, and then drop any courses they don't like.
Withdrawing means you've passed the drop deadline and your transcript will indicate that you withdrew from a class. If you're doing really poorly in a class, it's usually a good idea with withdraw from it. You'll get a W on your transcript but employers tend to be okay with a couple of them. In most cases, it's better to have a W than a D or an F.