After confirming both my Production and DR apps were running, I provisioned and deployed a Traffic Manager resource in South Central US and housed it in my Tertiary Resource Group. During provisioning, I configured my WebAppProd and WebAppDR apps as endpoints. WebAppProd was given a priority of 100 and WebAppDR a priority of 200.
I named the Traffic Manager Resource myazureapp.trafficmanager.net and configured it for "Priority Mode" so it would always send traffic to my production app unless the production app went down. I also set the DNS TTL value to 2 minutes so if there was a failure, it would only take two minutes or so for the DNS name to be re-requested and updated to reflect the DR app.
To test basic functionality, I connected to my production database with SQL Server Management Studio and created a small table. After creating the table, I wrote a small .php script to read from the table that I created and uploaded the script to my production web app via FTP. I created a similar script for my DR app but configured it to read from my DR database. Once both scripts were uploaded, I simply browsed to them with Google Chrome to ensure the read was successful in both production and DR.
NOTE: I had to add my laptop's public IP address to the firewall rules for both database servers before I could connect to them with SQL Server Management Studio.
With everything in place as far as functionality and DR went, I registered mydomainname.com, assigned it to my Traffic Manager, and updated my DNS so my users could access the website using my custome domain name.