How can I screencast what I am watching on television to a computer or laptop?

you can't. they are specifically designed to prevent that.

It is mostly done by hardware. And HDMI might prevent that on copyright ground; if the TV signal comes in as Composite (RCA red/white/yellow) it is much cheaper; but HDMI is not a cheap setup. Plus the fact laptops have no current HDMI in options.

Though I do have a laptop HDMI in option since I am using an old Core i7 that has ExpressCard option and I hold such card. I am not certain why the industry killed it. Composite inputs are smaller requirement in bandwidth so USB capture sticks abound.

You need a TV that is capable of working as a casting device, not many are. Even if they are it's common that any content that is copyright protected will not cast!

Some TVs that can cast perform the connection sequence backward compared to normal casting or may require a special app on the receiving device.

*I can cast from my TV to my laptop or phone, but it's unreliable. It's far more reliable casting from the TV to my tablet, possibly because they are the same brand (and have a helper app).

**It's not really that useful a function. I have to mute the sound from one device or the other, there is around a 1 sec delay on the device you are casting to!

There's a print screen button on your computer keyboard

When you pressed this button open the Paint software and press CTRL + V on your keyboard to paste it