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 functions 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

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 gr As Graphics, ByVal the_pen _
    As Pen, ByVal dt As Single, ByVal pt0 As PointF, ByVal _
    pt1 As PointF, ByVal pt2 As PointF, ByVal pt3 As PointF)
    ' Debugging code commented out.
    ' Draw the control lines.
    Dim dashed_pen As New Pen(Color.Black)
    dashed_pen.DashStyle = Drawing2D.DashStyle.Custom
    dashed_pen.DashPattern = New Single() {4, 4}
    gr.DrawLine(dashed_pen, pt0.X, pt0.Y, pt1.X, pt1.Y)
    gr.DrawLine(dashed_pen, pt2.X, pt2.Y, pt3.X, pt3.Y)
    dashed_pen.Dispose()

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

    t = 0.0
    x1 = X(t, pt0.X, pt1.X, pt2.X, pt3.X)
    y1 = Y(t, pt0.Y, pt1.Y, pt2.Y, pt3.Y)
    t += dt
    Do While t < 1.0
        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)
        gr.DrawLine(the_pen, x0, y0, x1, y1)
        t += dt
    Loop

    ' Connect to the final point.
    t = 1.0
    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)
    gr.DrawLine(the_pen, x0, y0, x1, y1)
End Sub