How do I write a script to install MySQL server on Ubuntu?

sudo apt-get install mysql will install, but it will also ask for a password to be entered in the console.

How do I do this in a non-interactive way? That is, write a script that can provide the password?

#!/bin/bash
sudo apt-get install mysql  # To install MySQL server
How to write script for assigning password to MySQL root user
End

sudo debconf-set-selections <<< 'mysql-server mysql-server/root_password password your_password'
sudo debconf-set-selections <<< 'mysql-server mysql-server/root_password_again password your_password'
sudo apt-get -y install mysql-server

For specific versions, such as mysql-server-5.6, you'll need to specify the version in like this:

sudo debconf-set-selections <<< 'mysql-server-5.6 mysql-server/root_password password your_password'
sudo debconf-set-selections <<< 'mysql-server-5.6 mysql-server/root_password_again password your_password'
sudo apt-get -y install mysql-server-5.6

For mysql-community-server, the keys are slightly different:

sudo debconf-set-selections <<< 'mysql-community-server mysql-community-server/root-pass password your_password'
sudo debconf-set-selections <<< 'mysql-community-server mysql-community-server/re-root-pass password your_password'
sudo apt-get -y install mysql-community-server

Replace your_password with the desired root password. (it seems your_password can also be left blank for a blank root password.)

If you writing a script then your shell may be not bash but dash/ash or some basic unix shell. These shells, unlike zsh, ksh93 and bash, doesn't support here-strings <<<. So you should use:

echo ... | sudo debconf-set-selections 

Or a more readable print of multiline strings:

cat << EOF | sudo debconf-set-selections
mysql-server mysql-server/root_password password your_password
mysql-server mysql-server/root_password_again password your_password
EOF

You can check with debconf-get-selections command:

$ sudo debconf-get-selections | grep ^mysql
mysql-server    mysql-server/root_password_again    password    your_password
mysql-server    mysql-server/root_password  password    your_password