How do I select a complete dataGridView Row when the user clicks a cell of that row?

You need to set datagridview's SelectionMode to FullRowMode.

Note: In Visual Studio 2013 with .NET 4.5 the property is called FullRowSelect.

If you want the row selected programatically, you would use the datagridview's cell click event: shown in VB.net and C#

VB.Net

Private Sub dgvGrid_CellClick(sender as System.Object, e as System.Windows.Forms.DataGridViewCellEventArgs) Handles dgvGrid.CellClick
    If e.RowIndex < 0 Then
        Exit Sub
    End If

    intIndex = e.RowIndex
    dgvGrid.Rows(intIndex).Selected = True
Exit Sub

C#

private void dgvRptTables_CellClick(System.Object sender, System.Windows.Forms.DataGridViewCellEventArgs e)
{
    if (e.RowIndex < 0) {
        return;
    }

    int index = e.RowIndex;
    dgvGrid.Rows[index].Selected = true;
}

In the DataGridView properties, Set

• MultiSelect -> True
• SelectionMode -> FullRowSelect