For future readers of this post, there’s an updated guide using the latest version of osTicket.

An overview of osTicket installation using the latest version of osTicket - v1.10 (at the time of writing this post), using DigitalOcean’s Ubuntu 16.04 LAMP Stack.

1. Create Ubuntu 16.04 Droplet
2. Login to your droplet and run mysql_secure_installation.
3. Purge php7.0 or php 7.1. The command would be apt-get purge php7.0-common.
4. Add the proper PPA Repo - add-apt-repository ppa:ondrej/php
5. Run apt-get update - to update the repo

6. Install php 5.6 along with the osTicket require packages.

   apt-get install php5.6 php5.6-cli php5.6-mysql php-gettext php5.6-mbstring php-xdebug libapache2-mod-php5.6 php5.6-gd php5.6-imap php5.6-xml php5.6-intl php5.6-apcu unzip -y

7. Download and extract osTicket - go to the dowload page and retrieved the file path.

   Do a simple wget command to download the zip file and extract:
   http://osticket.com/sites/default/files/download/osTicket-v1.10.zip - to download.

   unzip osTicket-v1.10.zip -d osticket - to extract the file to osticket folder.

8. Copy all the files inside osticket/upload to /var/www/html and set proper file/folder permission.

   chown -R :www-data /var/www/html - to set group permission.

   find /var/www/html -type d -exec chmod 755 {} \; - to set permission for directories

   find /var/www/html -type f -exec chmod 644 {} \; - to set permission for files

   Copy the ost-sampleconfig.php:

   cd /var/www/html

   cp include/ost-sampleconfig.php include/ost-config.php

   chmod 666 include/ost-config.php

9. Create the database for osticket. Using the commandline, login as root and use your supplied mysql password. To retrieve your MySQL - If you haven’t changed your password: cat /root/.digitalocean_password

   To create a database and database user:

   mysql -u root -p; - to login

   then…

   create database ost; - you may change ost to any shortname you wish.

   grant all on ost.* to 'ost'@'localhost' identified by 'enter-your-password-here';

   flush privileges;

10. Fire up your favorite browser and type in your osTicket URL or IP Address of your VPS. If you want this installation to be your production environment, then you must have configured your DNS Record first.

Follow the install wizard and supply your database details and fillout all the necessary fields.

After the installation, you need to remove the setup folder and change back ost-config.php to 644 permission.

You could read the step-by-step guide which includes DNS Record setup in DigitalOcean, from the link below:
https://chubbable.com/osticket-vps-installation

Process failed by:

WARNING: The following packages cannot be authenticated!
libssl1.1 php5.6-common php5.6-json php5.6-opcache php5.6-readline php5.6-cli libapache2-mod-php5.6 libargon2-0 libsodium18 php7.2-common php7.2-json php7.2-opcache php7.2-readline php7.2-cli php7.2-phpdbg php-apcu
php-apcu-bc php5.6-xml php-pear php-gettext php-xdebug php5.6 php5.6-gd php5.6-imap php5.6-intl php5.6-mbstring php5.6-mysql
E: There were unauthenticated packages and -y was used without –allow-unauthenticated