Since 20 january 2015 Joomla a new service. At joomla.com you can build a free Joomla website. This service is offered in collaboration with Siteground webhosting who builds the entire server structure where all Joomla websites will be hosted. Another possibility is to use demo.joomla.org where you can register a 90 day trail website, also hosted by Siteground.
The differences between these services are that you have control of your extensions & templates t the 90 days version while the joomla.com version you ahave a fixed subdomain with a selection of extensions & templates, updates are installed automatically. Both services offer the possibility to move to a private domain with your own hosting.
Both possibilities have their own pros and cons What is the good thing is that starting with Joomla! is now a lot easier. If you want to read the official announcement, just click here.