We use Discord to play each other with our actual cards. Unlike digital methods like OCTGN or Tabletop Simulator, webcam play will obviously require some physical space to play in. It'll also require some sort of camera and microphone.

Cards
Unsurprisingly, playing over webcams does require you to have physical cards. It's completely acceptable to use proxies, including cards you printed at home. The general rule is "if your opponent can tell what it is, it's fine to use". You can read more on that in the Printing Cards guide.

Webcam
The easiest way to set up. When buying a webcam, try to make sure it at least supports 1080p, so that your cards can be readable. 720p can still work though, but you might have to remind your opponent about specifics more often (current damage totals, etc). Most all webcams will also have a built in microphones, so that covers your audio.

Phone & Other Device
If you don't have a webcam and can't get one, you could also use your mobile phone. The typical setup here is to aim your camera at your playmat & cards, then login to Discord with another device to see your opponent's view. This will also require a tripod or some other way to get your phone above your play area.