Note that for development, the TextSecure staging environment uses a self-signed certificate, which Chrome will complain is insecure. So first visit <https://textsecure-service-staging.whispersystems.org/> in your browser and allow the certificate.
Now, in the extension's options, you can register for TextSecure:
* Select "Register" under "I'm new to TextSecure".
* Enter a real phone number (Google Voice numbers work too) and country combination and choose to send an SMS. You will receive a real SMS.
* Enter the verification code you received by SMS.
You should now be able to use the extension. If you need to reset your development environment, open a browser console within the extension options page (or inspect `background.html`) and execute `localStorage.clear()` to clear out the settings.