GRANT ALL PRIVILEGES ON somedatabase.* TO someuser@'somehostname' IDENTIFIED BY 'password';
FLUSH PRIVILEGES;

mysql_connect('mysqlservername', 'someuser', 'password');

$server = '192.168.0.3';
$user = "foo";
$password = "bar";
$conn = mysql_connect($server, $user, $password);

<?php mysql_connect('IP of 2nd computer', 'username', 'password'); ?>