If you want to host it on third party server(like Amazon AWS) the easiest way would be to:
1) Create a backup of your odoo (from database manager)

2) Set up Ubuntu server

3) Install Odoo on the remote server (use this script if you like: https://github.com/Yenthe666/InstallScript ) and restore the backup you made in piint 1

4) Set up Apache (Tutorial: https://www.cier.tech/blog/blog-1/post/configuring-apache-for-odoo-4) or Nginx (Tutorial: https://www.cier.tech/blog/blog-1/post/configuring-nginx-with-odoo-5)

5) Log in to your domain provider and point the domain to your server IP

Thanks Kalpesh, I thought it would be as easy as Wordpress localhost to publish. do you think if I build a website using Odoo subdomain like mysite.odoo.com is as good as community  or enterprise site do?