SQL Server Data Tools (which is what you're using for your database project) can work in two ways:
If you look at those articles. you will see that for development purposes, in both cases a localdb instance is needed. The local server is a limited SQL Server Express installation, which comes by default with Data Tools. So all you need to do is install Data Tools. If you already did, then you have localdb support. More on this from MSDN:
Microsoft SQL Server 2012 provides a local on-demand server instance, called SQL Server Express Local Database Runtime, which is activated when you debug a SQL Server Database project. This local server instance can be used as a sandbox for building, testing and debugging your project. It is independent of any of your installed SQL Server instances, and is not accessible outside SQL Server Data Tools (SSDT).
The workflow, for a central development database, would be:
- Create the database project and distribute it to each developer.
- Developers work "offline" and add/remove objects from the database.
- Before submitting the changes to source control, each developer also syncs the local database changes with the central development database.
- The rest of the team gets the changes from source control, so no manual sync needed. Only a new localdb publish would be required.
Of course, there are many other things to consider: local data (see here about replicating data to the real database), and some features not supported by localdb (like full text search).
I've tried this flow and works really well if you learn to control it. You always get a consistent central development database, without intermediary and unstable modifications.