When you call TWC to order internet service, they will set up a time for the installer to come to your place and do the instillation.
They will check the line to make sure there's no extra noise, and that it will be capable of a competent digital signal.
They will then install the cable modem to a regular cable jack in your house/apartment/whatever. On the back of this modem is an ethernet port. You'll hook ethernet port on your computer right up to the port on the modem using a standard ethernet cable.
Once that's done, and the installer's configured your computer, you'll be off to the races, no extra hardware required.