I got new server and installed phpMyAdmin. But whenever I visit the phpmyadmin url it says:

Cannot load mysql extension. Please check your PHP configuration

How do I fix this problem under CentOS / RHEL / Fedora Linux Apache web server?

You need to install php-mysql which is a module for PHP applications that use MySQL databases. You may also need to install the following:

• php-mysql : Module for PHP applications that use MySQL databases
• php-gd : A module for PHP applications for using the gd graphics library
• php-mbstring : A module for PHP applications which need multi-byte string handling
• php-mcrypt : Standard PHP module provides mcrypt library support

Type the following command to fix your issue:
# yum -y install php-mysql
# service httpd graceful
OR
# apachectl -k graceful
No need to edit /etc/php.ini as php-mysql package comes pre configured with /etc/php.d/mysql.ini file:
# cat /etc/php.d/mysql.ini
Sample outputs:

; Enable mysql extension module
extension=mysql.so

Optional Modules

To install other modules type:
# yum -y install php-mbstring php-mcrypt php-gd
# service httpd graceful