To set up a free educational account (you can check out the differences yourself between an edu and public account, but basically and edu account allows you to make Prezi's private), you need to go http://www.prezi.com/pricing-6/edu and choose the free account. BE WARNED - this will requires verifying the email address as an educational account and then sends a confirmation email to the email address, so if your school filters student emails from external networks (as they probably are due to COPPA and CIPA) you will need to let your IT department know AHEAD of time so they can open the filter for emails coming from Prezi.
(In reality, when you set up your account, check out the domain address (the part after the @ symbol in the email) of the Prezi confirmation email, and give your IT department that domain, so they know what to allow through the filters.)
Alternatively, you could also set up multiple Prezi accounts at your institution (get some other teachers to set them, or ask your IT department to give you multiple email addresses) and then give the students those username/passwords. As long as they are not working on the same prezi on the same account. (i.e. if you have 3 students who want to work on the same prezi, they can do it, as long as each student is logged on to a different Prezi account.)