You can use your phone to send SMS to another country but you will have to use the country code for that country. A list with the country codes is available from Wikipedia's page. The number format you need to fill in to the Destination is: 00+Country Code+City Code+Phone number.
It should look something like: +44 1234 123123. Instead of "+" you can also use 00.
Also, you can send SMS from various services located on web. There are websites which allow you to send SMS internationally for free.