Get the tarball from the official Site Owncloud

wget https://download.owncloud.org/community/owncloud-10.0.6.tar.bz2

Extract

tar -xzf owncloud-10.0.6.tar.bz2

If you use Ubuntu 14.04 you might have PHP5.5 in use. You need PHP5.6 to run this version of Owncloud.
Install PHP5.6

add-apt-repository ppa:ondrej/php
apt-get update
apt-get install php5.6 php5.6-mbstring php5.6-mcrypt php5.6-mysql php5.6-xml php5.6-apcu php5.6-zip php5.6-gd php5.6-curl php5.6-bcmath php5.6-intl php5.6-soap php5.6-imagick php5.6-imap php5.6-memcache php5.6-ps php5.6-pspell php5.6-recode php5.6-snmp php5.6-sqlite3 php5.6-tidy php5.6-xmlrpc php5.6-xsl
a2dismod php5
a2enmod php5.6
service apache2 restart

Copy the owncloud folder to your apache2 documentroot

mv owncloud /var/www/

Make sure your webuser is the owner of the dir and its files

chown -R www-data:www-data /var/www/owncloud

Add the following to an existing siteconfig or create a new one

Alias /owncloud "/var/www/owncloud/"

<Directory /var/www/owncloud/>
  Options +FollowSymlinks
  AllowOverride All

 <IfModule mod_dav.c>
  Dav off
 </IfModule>

 SetEnv HOME /var/www/owncloud
 SetEnv HTTP_HOME /var/www/owncloud

</Directory>

Browse your site, enter your username and password, add the MySQL connection info and you are done.

If you cant access your website (/owncloud was not found), you might need to change your documentroot from /var/www/html to /var/www or copy your owncloud folder into /var/www/html

Add the following to your .htaccess

Header set Strict-Transport-Security "max-age=31536000"

OR

Add the following to your apache2 siteconfig

Header always set Strict-Transport-Security "max-age=31536000; includeSubDomains"