Install Windows 2008 R2, 2012 or 2012 R2 for you base Operating System (OS).
Patch your server using you internal patch server or Windows update.
Prerequisites for Exchange Server 2012 Edge (source)

Install the above prerequisites, following what is appropriate for your server OS.
Reboot Server after all prerequisites have been installed.
Before you begin the installation of the Edge Transport Role don’t forget to set your FQDN on your server name or you will get this error message:
Installation
Once you have that configured, run the installation for Exchange Server 2013 using the wizard provided, which is no different than for the CAS or Mailbox roles:
Click Next.
Wait for any updates and click Next.
Files begin to copy to the server.
Wait for Setup to initialize.
Click Next.
Click ‘Accept’ and then click ‘Next’.
Click ‘Next’.
Select the Edge Transport role and click Next.
Wait for the readiness checks to proceed. If all the checks are good, click Install.
Patiently wait for the installation to go through its paces. Notice there are significantly less steps for the Edge Role versus a combined role server (CAS/MBX) installation.
Click Finish. Usually I reboot the server here to make sure all changes were committed.
Edge Sync Setup
http://technet.microsoft.com/en-us/library/aa997438%28v=exchg.150%29.aspx
If you installed an Exchange 2010 Edge Server, then the rest of the steps should feel relatively similar. The only difference is that there is no GUI to check your config again. PowerShell is your only tool on the Edge role.>BR>
First, create a new Edge Sync Agreement:
Then import that agreement on a mailbox server:
Firewall Ports
Make sure that the following ports are opened to allow the Edge Role to function properly:
- TCP Port 25
- TCP port 50389
- TCP port 50636
Post Installation Tasks
- Configure Accepted Domains if not already completed
Configure Anti-Spam rules or Transport Agents on the Edge server. Below are the agents you can configure:
- Test mailflow
Interesting Bug in Setup
One thing that was noticed by a fellow MVP was that the Exchange 2013 SP1 setup has a bug in that if you have a single role server (CAS or MBX) and you re-run the setup program you can select the missing role (if a CAS server then Mailbox):
This has been submitted as a bug to Microsoft and I would not recommend doing this as it will result in an unsupported configuration.