Twilio is a great service. It allows you to send and receive automated calls and text messages for very reasonable prices. They also have a wonderful API that makes integration into your site or plugin a breeze.
You are given a unique Account SID and Account Token for each phone number you use; you use this data to authenticate with the server. To send a request, you just put To, From, and Body URL attributes into a HTTP post. The easiest way to do this is probably using cURL (or create stream). The function below is all you need to send an SMS.