To get started, you must first set up your own account on Twilio. Sign up at http://www.twilio.com. Within Twilio's system, you'll then:
Create your own account.
Provide a payment mechanism (usually a credit card).
Purchase at least one incoming phone number from them. You should get one in the same area code as your regular phone numbers, but this number cannot be the same as your regular phone number and must be acquired from Twilio.
Configure that phone number, within Twilio's website, to look like this. Note especially the SMS URL which is required by Twilio. The URL here does nothing and does not record your messages, but does act as a placeholder so that Twilio can know it's notified someone.