To begin, stop the database service and check the service status:

------------- SystemD -------------
# systemctl stop mariadb
------------- SysVinit -------------
# /etc/init.d/mysqld stop

Next, start the service with --skip-grant-tables:

------------- SystemD -------------
# systemctl set-environment MYSQLD_OPTS="--skip-grant-tables"
# systemctl start mariadb
# systemctl status mariadb
------------- SysVinit -------------
# mysqld_safe --skip-grant-tables &

This will allow you to connect to the database server as root without a password (you may need to switch to a different terminal to do so):

# mysql -u root

From then on, follow the steps outlined below.

MariaDB [(none)]> USE mysql;
MariaDB [(none)]> UPDATE user SET password=PASSWORD('YourNewPasswordHere') WHERE User='root' AND Host = 'localhost';
MariaDB [(none)]> FLUSH PRIVILEGES;

Finally, stop the service, unset the environment variable and start the service once again:

------------- SystemD -------------
# systemctl stop mariadb
# systemctl unset-environment MYSQLD_OPTS
# systemctl start mariadb
------------- SysVinit -------------
# /etc/init.d/mysql stop
# /etc/init.d/mysql start

This will cause the previous changes to take effect, allowing you to connect to the database server using the new password.