SSL on Azure Shared Plan?
There's a work around to Azure not allowing SSL on Shared web app plans with custom domains.
You can create your website with Azure shared plan, and use CloudFlare to route your traffic to your domain. So basically your domains DNS would point to CloudFlare and you would configure CloudFlare with your azure shared website.CloudFlare Free plan comes with a free SSL certificate. So essentially your traffic is SSL secured.
If you need SSL over your custom domain there's no way, at least on azure web Apps. You'll need to run the site in Basic plan.
The workaround:
Deploy your site in an Azure VM using the cheaper plan: A0 15 USD / month and configure there your IIS + SSL Certificate
Otherwise
If you need HTTPS using your azurewebsites domain (mysite.azurewebsites.net) this one IS included in service just use https to browse the website.
You will have to be on "Basic" plan in order to have SSL. see details from below link.
https://azure.microsoft.com/en-us/pricing/details/app-service/plans/