How to make MySQL handle UTF-8 properly

Question

One of the responses to a question I asked yesterday suggested that I should make sure my database can handle UTF-8 characters correctly. How I can do this with MySQL?

Answer 1

DATABASE CONNECTION TO UTF-8

$connect = mysql_connect('$localhost','$username','$password') or die(mysql_error());
mysql_set_charset('utf8',$connect);
mysql_select_db('$database_name','$connect') or die(mysql_error());