Log onto the Azure Portal, go to the App Services and select the App that you need to publish from Visual Studio to Azure.
Click on Get publish Profile. This downloads a Settings file.
In Visual Studio go to Publish and selete the "Import Profile" option.
Then import the Profile that you just exported from Azure. Done!
From here: https://microsoft.github.io/AzureTipsAndTricks/blog/tip140.html
Note by cbattlegear One important caveat to this process (as shown below). If any writes are happening on the database while you do the export the import will be broken. Best practice is to run CREATE DATABASE AS COPY
to create a copy of the database and create an export of the copy.
Right-click on the Database -> click Tasks > Export data-tier application
Now ensure you are connected to your local target SQL server instance (or SQL Azure instance) and right-click on the Database -> click Tasks > Import data-tier application and select the .backpac file that you created earlier.