p0 * (1 - t) ^ 3 +
    p1 * 3 * t * (1 - t) ^ 2 +
    p2 * 3 * t ^ 2 * (1 - t) +
    p3 * t ^ 3

Here t is a parametric variable that rannges from 0 to 1.

The following X and Y functions return values of this equation for values of t and the control points' coordinates. Subroutine DrawBezier loops variable t from 0 to 1, uses the functions to generate the points on the Bezier curve, and connects them.

' Parametric X function for drawing a degree 3 Bezier curve.
Private Function X(ByVal t As Single, ByVal x0 As Single, _
    ByVal x1 As Single, ByVal x2 As Single, ByVal x3 As _
    Single) As Single
    X = CSng( _
        x0 * (1 - t) ^ 3 + _
        x1 * 3 * t * (1 - t) ^ 2 + _
        x2 * 3 * t ^ 2 * (1 - t) + _
        x3 * t ^ 3 _
        )
End Function

' Parametric Y function for drawing a degree 3 Bezier curve.
Private Function Y(ByVal t As Single, ByVal y0 As Single, _
    ByVal y1 As Single, ByVal y2 As Single, ByVal y3 As _
    Single) As Single
    Y = CSng( _
        y0 * (1 - t) ^ 3 + _
        y1 * 3 * t * (1 - t) ^ 2 + _
        y2 * 3 * t ^ 2 * (1 - t) + _
        y3 * t ^ 3 _
        )
End Function

' Draw the Bezier curve.
Public Sub DrawBezier(ByVal pic As Object, ByVal dt As _
    Single, pt0 As PointF, pt1 As PointF, pt2 As PointF, _
    pt3 As PointF)
    ' Debugging code.
    ' Draw the control lines.
    Dim p As PictureBox
    pic.DrawStyle = vbDot
    pic.Line (pt0.X, pt0.Y)-(pt1.X, pt1.Y)
    pic.Line (pt2.X, pt2.Y)-(pt3.X, pt3.Y)
    pic.DrawStyle = vbSolid

    ' Draw the curve.
    Dim t As Single
    Dim x0 As Single
    Dim y0 As Single
    Dim x1 As Single
    Dim y1 As Single

    t = 0#
    x1 = X(t, pt0.X, pt1.X, pt2.X, pt3.X)
    y1 = Y(t, pt0.Y, pt1.Y, pt2.Y, pt3.Y)
    t = t + dt
    Do While t < 1#
        x0 = x1
        y0 = y1
        x1 = X(t, pt0.X, pt1.X, pt2.X, pt3.X)
        y1 = Y(t, pt0.Y, pt1.Y, pt2.Y, pt3.Y)
        pic.Line (x0, y0)-(x1, y1)
        t = t + dt
    Loop

    ' Connect to the final point.
    t = 1#
    x0 = x1
    y0 = y1
    x1 = X(t, pt0.X, pt1.X, pt2.X, pt3.X)
    y1 = Y(t, pt0.Y, pt1.Y, pt2.Y, pt3.Y)
    pic.Line (x0, y0)-(x1, y1)
End Sub