What is the best way to create a smooth curve path from a set of points? For example:
I've seen Bezier curves before, but those try to smooth out the path from the set of points, like this:
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There are multiple types of Splines, Bezier curves are one of them. Beziers aren't required to pass through the points that define them. From the looks of it, you want a regular cubic spline. It will ensure that the line crosses through the points specified. You can find some interactive examples of different types here.
Also, I know you're busy being an 80's guy, but get that boneitis checkout ASAP.
You may want Catmull-Rom splines. They go through every point (unlike Bezier curves, which don't go through the control points).