Watching Cable TV on Computer Monitor?

Hey everyone, I'm looking to buy a monitor for my new computer. Its an HD LED 1080p monitor with DVI and VGA inputs. I'm wondering if I can somehow hook up my TV cable (Timewarner if it matters) to my monitor. I've tried to research DVI and have gotten some mixed results in my searches. Could someone give me a simply answer to this question? If I can hook up cable to my monitor, could you please tell me how? I don't have enough cash for a big enough HDTV so please don't just tell me to get one of those instead. Thanks.