You may (or may not) have a requirement to setup a linked server to Azure SQL Database from a locally installed SQL Server. One reason could be to pull down some reports from an Azure SQL Database to a local file share. Whatever your reason is hopefully you will find this blog post useful because I ran into some complications on the way.
This is what your linked server creation screens in SSMS (SQL Server Management Studio) should look like.
Take advantage of Arun’s hard-earned experience and read his post.