Twine uses a carrier's SMS email gateway to handle text messages. If the recipient's carrier is on this list, then there's a good chance you'll be able to send an SMS:
If yours isn't listed and they do have a gateway, please send the details our way!
When you first power up your Twine, it will create its own wireless network that you can connect to for configuration (including security setup). Once that is done, Twine will connect to your local WiFi network and the internet!
Don't see the answer to your question? Ask the project creator directly.