A Exchange hybrid server is not a special role nor a special installation of Exchange 2013.
A hybrid server is a regular Exchange 2013 with CAS and Mailbox role.
The purpose of the hybrid server is to have rich co-existence between the internal Exchange environment and Exchange Online and mostly for migrating the internal mailboxes to Exchange Online.
Microsoft offer customers a free hybrid server license. Well actually multiple licenses if needed and of course that is required for redundancy.
You cannot use these hybrid servers for hosting mailboxes since this is not included in the license agreement. This also only applies for Office 365 customers that have a paid enterprise subscription.
So, download the Exchange 2013 bits and install it as per instructions on TechNet. You install a new server and add Exchange 2013 to the organization, just like an upgrade.
Get the key from Microsoft here. You need your Office 365 admin account.
If the on-prem servers is Exchange 2003, you can only use Exchange 2010 SP3 servers as hybrid. Any deployment with Exchange 2007 or later should use Exchange 2013 SP1 as hybrid servers.