Its not linux which will send the sms... sounds like you already sent sms from windows...!!!
Linux will come only in picture at the level where you application connects to the message center(SMS service provider) using an identification module (SIM)
There will be many components in such an application, in a broad sense....
An interface/API to be able to connect to a telephone service provider running a message center.
An interface to use your computer to send/receive data from the message center.
An interface to the user wherein he types and interacts with the system.