Let I try to explain through example. Let's start to add single value and this is how you can do it.
update_option( 'my_data', 'my_value' );
Like the my_value you can pass the array variable. Consider with the next example.
$data = array();
$data['my_key_1'] = 'my_value_1';
$data['my_key_2'] = 'my_value_2';
update_option( 'my_data', $data );