I assume you have already a mysql user which password want to update or change. You will need to login into your mysql server with your root user which has administrative privileges. So, follow below steps and you will easily be able to update the user password:
1- Open the command shell and connect to the mysql server as root user
mysql -u root -h localhost -p
2- Run command
ALTER USER 'user_name'@'localhost' IDENTIFIED BY 'New password here';
You will just need to put your user name and password to update for the user.