How do I enable SMS notifications in my web apps?
I don't have any knowledge in this area. But I think you'll have to talk to the mobile operators, and see if they have any API for sending SMS messages. 
You'll probably have to pay them, or have some scheme for customers to pay them. Alternatively there might be some 3rd party that implements this functionality.
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.