Given 3 points, how do I calculate the normal vector?

It depends on the order of the points. If the points are specified in a counter-clockwise order as seen from a direction opposing the normal, then it’s simple to calculate:

Dir = (B - A) x (C - A)
Norm = Dir / len(Dir)

where x is the cross product.

If you’re using OpenTK or XNA (have access to the Vector3 class), then it’s simply a matter of:

class Triangle {
    Vector3 a, b, c;
    public Vector3 Normal {
        get {
            var dir = Vector3.Cross(b - a, c - a);
            var norm = Vector3.Normalize(dir);
            return norm;
        }
    }
}