Setting up mysql password is one of the essential tasks. By default root user is MySQL admin account. Please note that the Linux / UNIX login root account for your operating system and MySQL root are different. They are separate and nothing to do with each other (indeed some admin removes root account and setup admin as mysql super user).
mysqladmin command to change root password

If you have never set a root password for MySQL, the server does not require a password at all for connecting as root. To setup root password for first time, use mysqladmin command at shell prompt as follows:

$ mysqladmin -u root password NEWPASSWORD

However, if you want to change (or update) a root password, then you need to use following command

$ mysqladmin -u root -p’oldpassword’ password newpass

For example, If old password is abc, and set new password to 123456, enter:

$ mysqladmin -u root -p’abc’ password ’123456′

Change MySQL password for other user

To change a normal user password you need to type (let us assume you would like to change password for vivek):

$ mysqladmin -u vivek -p oldpassword password newpass

Changing MySQL root user password using MySQL sql command

This is another method. MySQL stores username and passwords in user table inside MySQL database. You can directly update password using the following method to update or change password for user vivek:

1) Login to mysql server, type following command at shell prompt:

$ mysql -u root -p

2) Use mysql database (type command at mysql> prompt):

mysql> use mysql;

3) Change password for user vivek:

mysql> update user set password=PASSWORD(“NEWPASSWORD”) where User=’vivek’;

4) Reload privileges:

mysql> flush privileges;
mysql> quit

This method you need to use while using PHP or Perl scripting.