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First you need to install the Microsoft SQL Server Driver for PHP 1.1. You can install this from the Web Platform Installer (www.microsoft.com/web) or just go search for the download site.

Make sure you have created the DB in SQL Azure. Create your acount in sql.azure.com.
Your database will have a randomly generated name that ends with the domain .database.windows.net.

In order to connect, you can create a new Windows Azure Web Project in Eclipse, and select SQL Azure in the Data Storage Options of the dialog form.

Right mouse click on the Azure project (not the web role), click Properties, look under Windows Azure, you will find SQL Azure. Type in the following info.

Hostname: servername.database.windows.net
Database: master (this is the default DB)
username: user@servername (your username as created in sql.azure.com)
password: your password (as created in sql.azure.com)

Took me awhile to figure out that I need to have username@servername. IT works!