When you host your application Azure you don’t get SMTP server or any other mail services.
So you got 2 choices. 1) Host your own SMTP server or 2) Use SendGrid where you can get 25000 emails/month for free.
Start by registering for SendGrid in this url.
Fill in the form and create your account. (Doesn’t require credit card).
It will take them a while to provision you an account. If you have any problems with provisioning don’t hesitate to send email to help@sendgrid.com. They are very fast to fix your problem.
While it’s provisioning create a new WCF application. Remember to choose .net 4.0
After that right click project and click manage nuget references
Then search for SendGrid and install it. Now edit IService1.cs and Service1.svc
Now you can send emails easily from your Azure application. You can find the published WCF service from url