"Like just using the usual plug into the wall cable" - no, that is a coaxial connection and requires a TV tuner. Computer monitors do not come with this. But you could buy a TV tuner card/add-on for a computer and then feed your TV into your computer (and then see it on the computer monitor).
Otherwise, to use a computer monitor as a TV, you need to see what kind of TV related inputs it might have. Does it have composite RCA (yellow, red/white)? Does it have HDMI? If it has a TV related input, then using a DTV converter or a cable/satellite set top box, you could then feed the computer monitor a TV signal yes. Just make up cable types and you're good to go.
Note that computer monitors might not be the same aspect ratio as your TV. If you have an old "square-ish" computer monitor, that is the same aspect ratio as an old CRT/tube television (both are 4:3). But if you have moved into wide-screen at all, then you could run into a discrepancy. Most widescreen computer monitors are actually an aspect ratio of 16:10. But widescreen TVs are 16:9. Its not a huge difference, but there is some. So you could get some minor letterbox (black bars top and bottom) or some minor distortion (probably not noticeable, but it would be there).
Also, not a lot of computer monitors have built-in speakers. So where are you going to listen to the TV? You might have to buy add-on "soundbars" or such for the computer monitor in order to use it as a TV.