How to access MySQL (version 5.0.45) remotely

In MySQL server side(assuming the MySQL server IP is 192.168.1.1), create a user and grant the remote access privilege to the new created user.

mysql> use mysql;
mysql> GRANT ALL ON *.* TO admin@'%' IDENTIFIED BY 'adminpwd' WITH GRANT OPTION;

Comments:
Here, admin@'%' means allow user 'admin' to connect with this MySQL from any IP address remotely.

Then we can try to connect to MySQL server 192.168.1.1 from any MySQL client.
mysql -h192.168.1.1 -uadmin -padminpwd