On local SQL Server database right-click on the database, Tasks, then Export Data-Tier Application to create a *.bacpac file.

Connect to the Azure database server via SSMS. Right-Click on the Azure Databases node. The Database cannot currently exist, so if it does it needs to be deleted first!

Select Import Data-tier Application and select the *.bacpac files that was created in the first step. This creates the database in Azure!

Don't forget to select the Edition of Microsoft Azure SQL Database before you complete the process.