Can I try Amazon EC2 for free?

Solution 1:

After November the 1st, you can sign up for the Free usage tier:

Beginning November 1, new AWS customers will be able to run a free Amazon EC2 Micro Instance for a year, while also leveraging a new free usage tier for Amazon S3, Amazon Elastic Block Store, Amazon Elastic Load Balancing, and AWS data transfer. AWS’s free usage tier can be used for anything you want to run in the cloud: launch new applications, test existing applications in the cloud, or simply gain hands-on experience with AWS.

Solution 2:

Amazon EC2 is a server rental. The rental fee is by hour of rental, you also have to pay for the bandwidth your server uses. See their pricing page for more information.