Add up the angles between the point in question and adjacent points on the polygon taken in order. If the total of all the angles is 2 * PI or -2 * PI, then the point is inside the polygon. If the total is zero, the point is outside. You can verify this intuitively with some simple examples using squares or triangles.

' Return True if the point is in the polygon.
Public Function PointInPolygon(ByVal points() As PointF, _
    ByVal X As Single, ByVal Y As Single) As Boolean
    ' Get the angle between the point and the
    ' first and last vertices.
    Dim max_point As Integer = points.Length - 1
    Dim total_angle As Single = GetAngle( _
        points(max_point).X, points(max_point).Y, _
        X, Y, _
        points(0).X, points(0).Y)

    ' Add the angles from the point
    ' to each other pair of vertices.
    For i As Integer = 0 To max_point - 1
        total_angle += GetAngle( _
            points(i).X, points(i).Y, _
            X, Y, _
            points(i + 1).X, points(i + 1).Y)
    Next i

    ' The total angle should be 2 * PI or -2 * PI if
    ' the point is in the polygon and close to zero
    ' if the point is outside the polygon.
    Return Math.Abs(total_angle) > 0.000001
End Function