phpMyAdmin can connect to a remote database just by setting it up with the host, user and password of the remote machine. As long as the MySQL port is open in the host, the MySQL running there is configured for allowing network connections, and your user has permission for being connected remotely.
From the machine running phpMyAdmin or any other machine (not the MySQL server), run the command line client to test if connection is possible:
$ mysql -h<ip> -u<user> -p<password> <database>
Where ip is the MySQL server IP, database is the name of your database and user and password are the credentials of your user in MySQL. This should give you the mysql client prompt on success. Or a proper description of the error.
MySQL server is usually configure for listen to a local socket only. It doesn't bind ti 3306 TCP port by default. In order to configure it properly you have to edit server's configuration file (usually /etc/my.cnf)
bind-address = 10.0.0.5
You have to replace the IP in this example with your server's IP address. And you have to check that option "skip-networking" is not activated. Because that would prevent MySQL binding the IP configured.
After rebooting you can check whether MySQL is listening with this command in a server's shell:
# netstat -nap | grep mysqld
tcp 0 0 10.0.0.5:3306 0.0.0.0:* LISTEN 3547/mysqld
unix 2 [ ACC ] STREAM LISTENING 13554 3547/mysqld /var/lib/mysql/mysql.sock
You have to see a line like the first output here. The 3306 number is the default MySQL port and you have to open it for incoming TCP connections, if you have a firewall protecting the server.
After this you should be able to connect to MySQL. But yet you may have problems loging in if your permissions are not properly set. MySQL users have user name and host in the form user@host, thus if you create a user my_user@localhost and you try to login from anything different of localhost, access will be denied. Let's think your client is running over a machine with IP address 10.0.0.33 and you want to give permission to access a database. Your user must be firstname.lastname@example.org or my_user@% being the second one an unrestricted user for connecting from any machine. Which is better to avoid if you know beforehand the IP of your client.