How do I enable SMS notifications in my web apps?
The easiest way to accomplish this is by using a third party API. Some I know that work well are:

restSms.me
Twilio.com
Clicatell.com

I have used all of them and they easiest/cheapest one to implement was restSms.me
Hope that helps.
I have a web application and I would like to enable real time SMS notifications to the users of the applications. 
Note: I currently cannot use the Twitter API because I live in West Africa, and Twitter doesn't send SMS to my country.
Also email2sms is not an option because the mobile operators don't allow that in my country.