At this time, Star citizen does not offer a free trial for the game.
However, we do occasionally run special events where anyone can explore the 'verse for a limited time: Free Fly Events.
What is a Free Fly Event?
A Free Fly is a special event that occurs now and then that will allow anyone who wishes to login and try out the game without making a monetary pledge of support for the Star Citzen project. During this time period, players will not require a Game Package on their RSI account to login and play on the Star Citizen Alpha Test servers. A basic ship is provided to everyone so that they have some means of exploring the stars, with the exact model provided varying by event.
These events generally run for a week or slightly longer, depending on the length of the in-game event it is tied to.
How do I know if there is a Free Fly event happening?
The easiest way is to check the RSI website and the recent Commlink announcements. If we are running one of these events, there will be a link to the Free Fly page there.
We also always publish a Free Fly Knowledge Base article which goes over the basics for that event and links to all relevant pages to join in. If a Free Fly is active, you can check the Announcements section to see if our article is there.