Please make sure you install the service with a User Account with the appropriate permissions to access the SQL database with windows authentication.
The installation steps are the same for ExSync Service as for the ExSync Application.
The main difference you will notice is that the 'basic scheduler' menu is removed, as this will be set up in Windows Scheduler.
ExSync Application:
ExSync: Service
You can follow all the installation steps to install ExSync: Service here.
Once you have finished these steps, you can refer to the the next steps following this guide for Service specific configuration.