How do I start/stop mysql server?

Your first two commands weren't run as root so that is expected behaviour. You need to be root to stop/start mysql.

However:

sudo /etc/init.d/mysql start

should work. Indeed it does, for me:

kojan:~> sudo /etc/init.d/mysql restart
[sudo] password for chris: 
Stopping MySQL database server: mysqld.
Starting MySQL database server: mysqld.
Checking for corrupt, not cleanly closed and upgrade needing tables..

I used restart rather than start, since it was already running, but the effect is the same. Are you sure you entered your password correctly? :) Have you edited your sudo config at all which would stop this working?

This one..

sudo /etc/init.d/mysql - root -p start

The arguments are wrong. an init.d script only takes start or stop or restart - just one word telling it what to do. You cannot give it multiple arguments as you were trying to do.

Anyway, the short answer is the one you actually got to work, is the recommended way. service is replacing all the init.d scripts over time, so you should get into the habit of using service. The page you link is 3 years old so has to be taken with some salt :)

Also helps to double check that "mysql" is the correct service name. In my case it wasn't. I kept getting following response: mysql: unrecognized service when running

service mysql status 

Then I checked /etc/init.d and found script named mysqld which listed process name: mysqld and prog=mysqld

So then I did

service mysqld status
service mysqld stop
service mysqld start 

and they all worked fine.

For Ubuntu 12.10 to 14.04 (Upstart)

Newer versions of Ubuntu use systemd.

START MYSQL:

sudo start mysql

RESTART MYSQL:

sudo restart mysql # The service must be running

STOP MYSQL:

sudo stop mysql # The service must be running