Can I use "Homegroup"?

I have a laptop with Windows 10, and I just got a Roku TV, which is my very first flat screen. I was hoping to be able to connect my laptop to the TV. I don't have an HDMI cable yet, but plan on getting one tomorrow.

But I was trying out other ways of doing it first. One thing I tried was creating a "Homegroup" in the Network section of Win10. When I was done, it showed that there was an active connection between my laptop and my TV. The network or homegroup name even included the word "Roku" in the title, and showed information being sent and received. But that's all the activity I could find. On the TV, I saw no menus or options telling me to do anything, even though there was an instruction on my laptop saying to follow the direction on the TV.

So, how does this work?
BTW, I don't have internet at home, and I don't have a router. Also, the TV doesn't have Bluetooth, but it does have Wi-fi.

The first thing is forget home group as the next update removes it from Windows so you won't be able to use it

Bree said:

You can right-click on a media file, video (eg. mp4, wmv. etc.) or audio (mp3, wav, etc.) and 'Cast to' a device like a TV.

Add or Remove Cast to Device context menu in Windows 10

If both the PC and TV support Miracast, you can project your PC's screen to the TV.

Check Miracast Support on Windows 10 PC
Connect to Wireless Display with Miracast in Windows 10

I forgot to mention that I did try to "Cast to" with different files, and it gave me a few options which included my TV, but it didn't do anything but start playing the file on my computer. Is there something I should have done with the TV?

Samuria said:

The first thing is forget home group as the next update removes it from Windows so you won't be able to use it

I haven't been doing updates for the last couple months, so I'm safe for now.

Bree said:

Works for me (and that's without having a Homegroup, just the default Workgroup networking) but then I do have a router and therefore a home network.

I'm getting the impression that I'd need a router, and perhaps internet. I was hoping that my laptop's Wi-fi would simply connect to my TV's Wi-fi and just work directly between one another. From what I saw of my homegroup connection, there was information going back and forth, so it looked like they were connected. I just don't know how to actually make anything happen, such as Casting something from the computer to the TV. Is there a certain menu I have to have on screen? I did have the Network scan on the screen, and it showed a number of my neighbors' secured Wi-fi signals, but not my TV--even when I searched multiple times.