Local over-the-air (OTA) broadcasts require an ATSC tuner to receive them. Unfortunately Hollywood has done a pretty good job exterminating most of them from the market. If your TV won't accept digital signals, then you need a digital converter box with ATSC tuner. Hollywood hasn't been as concerned about those because the output is an inferior analog format.
If you want to watch the local channels on your cable TV cable (they're required to carry these by law in the U.S.), then what you need depends on the cable company. Some of them still transmit analog channels, and your TV can view them if it's capable of tuning in to analog cable TV channels (most VCRs can, so scrounge up a VCR on craigslist if your TV can't). Others use digital cable TV channels, which requires a set-top box to tune. Some use encrypted digital cable TV channels. Unfortunately these require a cable TV subscription to decode (cheapest way is to buy your own set-top box and rent a CableCard from the cable company).