How to send SMS from a website to a mobile phone?
Google might help you with this request because there is a plenty of websites that allow you to send SMS messages using a simple website. For this purpose, check this Google search query and use a website to send SMS across the world.
there a plenty of websites that allow you to send SMS messages,one of them is way2sms and below is the link
You can integrate sms function to your website with a SMS API.
Which programming language you wish to use?
Here's an example for sending / receiving text messages in your website:http://www.ozekisms.com/index.php?owpn=204&info=php_sms_example
I hope i can help you!