Private Sub Button1_Click(ByVal sender As Object, ByVal e As EventArgs) _
Handles Button1.Click
    If RadioButton1.Checked = True Then
        DataGridView1.Sort(New RowComparer(SortOrder.Ascending))
    ElseIf RadioButton2.Checked = True Then
        DataGridView1.Sort(New RowComparer(SortOrder.Descending))
    End If
End Sub

Private Class RowComparer
    Implements System.Collections.IComparer

    Private sortOrderModifier As Integer = 1

    Public Sub New(ByVal sortOrder As SortOrder)
        If sortOrder = sortOrder.Descending Then
            sortOrderModifier = -1
        ElseIf sortOrder = sortOrder.Ascending Then

            sortOrderModifier = 1
        End If
    End Sub

    Public Function Compare(ByVal x As Object, ByVal y As Object) As Integer _
        Implements System.Collections.IComparer.Compare

        Dim DataGridViewRow1 As DataGridViewRow = CType(x, DataGridViewRow)
        Dim DataGridViewRow2 As DataGridViewRow = CType(y, DataGridViewRow)

        ' Try to sort based on the Last Name column.
        Dim CompareResult As Integer = System.String.Compare( _
            DataGridViewRow1.Cells(1).Value.ToString(), _
            DataGridViewRow2.Cells(1).Value.ToString())

        ' If the Last Names are equal, sort based on the First Name.
        If CompareResult = 0 Then
            CompareResult = System.String.Compare( _
                DataGridViewRow1.Cells(0).Value.ToString(), _
                DataGridViewRow2.Cells(0).Value.ToString())
        End If
        Return CompareResult * sortOrderModifier
    End Function
End Class

private void Button1_Click( object sender, EventArgs e )
{
    if ( RadioButton1.Checked == true )
    {
        DataGridView1.Sort( new RowComparer( SortOrder.Ascending ) );
    }
    else if ( RadioButton2.Checked == true )
    {
        DataGridView1.Sort( new RowComparer( SortOrder.Descending ) );
    }
}

private class RowComparer : System.Collections.IComparer
{
    private static int sortOrderModifier = 1;

    public RowComparer(SortOrder sortOrder)
    {
        if (sortOrder == SortOrder.Descending)
        {
            sortOrderModifier = -1;
        }
        else if (sortOrder == SortOrder.Ascending)
        {
            sortOrderModifier = 1;
        }
    }

    public int Compare(object x, object y)
    {
        DataGridViewRow DataGridViewRow1 = (DataGridViewRow)x;
        DataGridViewRow DataGridViewRow2 = (DataGridViewRow)y;

        // Try to sort based on the Last Name column.
        int CompareResult = System.String.Compare(
            DataGridViewRow1.Cells[1].Value.ToString(),
            DataGridViewRow2.Cells[1].Value.ToString());

        // If the Last Names are equal, sort based on the First Name.
        if ( CompareResult == 0 )
        {
            CompareResult = System.String.Compare(
                DataGridViewRow1.Cells[0].Value.ToString(),
                DataGridViewRow2.Cells[0].Value.ToString());
        }
        return CompareResult * sortOrderModifier;
    }
}