From ownCloud.org

These are the instructions for Debian/Ubuntu based distros. For other Linux distributions use suitable package installer like yum.

• install apache
  sudo apt-get install apache2
• install php5
  sudo apt-get install php5
• For database you can either use MySQL or SQLite
  sudo apt-get install mysql-server php5-mysql
sudo apt-get install sqlite php5-sqlite
• download owncloud
  git clone git://gitorious.org/owncloud/owncloud.git
• copy ownCloud to apache server directory (/var/www in most cases)
  sudo cp -r owncloud /var/www
• make ownCloud directory accessable to apache
  cd /var/www
sudo chown -R www-data:www-data owncloud

(If you're using mysql, you have to set the database character set to something else then utf-8, for example latin1 otherwise some keys will be to long for mysql)

After this open the server directory in which ownCloud is extracted in your favorite browser. The browser will show you the first run wizard. Here you can choose between MySQL and SQLite. Provide all the required details and hit the save button. That is it! You have installed ownCloud successfully. If you face any problems please drop in at #owncloud on Freenode. We will be glad to help you.

If have followed the steps above and want to try it out, run this command in a terminal to start Apache if it's not already running:
sudo /etc/init.d/apache2 start
Then go to http://127.0.0.1/owncloud/index.php and set it up. Hit the enter key to submit the details in the form.

Configure Apache

If you already have a website running from Document Root but would still like to install OwnCloud you can use a Name-based virtual host entry and subdomain.

Edit your DNS record following this example: point owncloud.foo.com > ip.ip.ip.ip

CENTOS5

Create a new file in /etc/httpd/conf/ and call it owncloud.conf.

You can use the following as an example.

 
<IfModule mod_alias.c>
Alias /owncloud /var/www/owncloud/
</IfModule>
<Directory /var/www/owncloud/>
   Options None
   Order allow,deny
   allow from all
</Directory>
<VirtualHost *:80>
    ServerAdmin foo@foofarm.com
    DocumentRoot /var/www/html/owncloud
    ServerName owncloud.foo.com
    ErrorLog logs/owncloud.foo.info-error_log
    CustomLog logs/owncloud.foo.info-access_log common
</VirtualHost>

Now edit your httpd.conf file which is usually located in /etc/httpd/conf/httpd.conf

Add the following to the bottom

 Include /etc/httpd/conf/owncloud.conf 

Restart apache and now when you point your browser to owncloud.foo.com it should properly load without disturbing foo.com.