It will depend on where you are.
There are TV tuner cards (a Google/Bing search will show up a whole range). You need input to get them to work.
For terrestrial broadcast just plug in the coaxial cable from your aerial (antenna) and you should be good to go.
For satellite and cable its more complicated. Unless you're in an area that can receive free satellite broadcasts (Freesat in the UK) you'll need a subscription and a tuner that can be activated to unscramble the signals. I don't know whether these are available as separate cards.
If you're watching via TV card then you should be able to browse the internet OK as the signal won't be consuming any of your bandwidth. You might have processor issues - but that
will depend on what PC and TV card you have.
Though you don't want online TV the following information might be useful
You can also watch TV over the internet (BBC iPlayer etc in the UK), but with these you need an IP address in the locale covered by the service.
If you are watching via the internet then the streamed video will be consuming a fair amount of your bandwidth. So if you try to browse the internet you might experience problems with either the browsing, the video stream (pausing/buffering) or both.