Cable-based internet access is provided through a device called a "cable modem".  Time Warner will automatically provide a cable modem to you, and charge you a monthly fee for its use (i.e. you are leasing it).  However, cable modems are commodity equipment, and it is entirely possible to purchase your own cable modem (as you would your own wireless/home router) and avoid Time Warner's rental fee.

Installation of a cable modem is relatively straightforward if you are comfortable installing other home/office network equipment.  The trade-off is that you must 1) purchase the equipment up-front 2) be liable for its maintenance (which is usually minimal).

See the following resources for more information: