In a nutshell, it's the same as you would do in Photoshop. Resolve has all of the same blending modes as Photoshop does. In fact, any blending mode is just one of a limited number of ways its mathematically possible to combine one image layer with another.
The main difference between compositing images in Photoshop and Resolve is that in the latter, movement presents additional challenges. So more accurately, yes Resolve is like Photoshopping an image, but it's like doing it 24 to 60 times every second.
The easiest way to accomplish this depends on your footage. In the above image, yes, you could cut out the TV screen and plop something into the hole. But it would probably look bad if that was all you did, and the same is true for Photoshop. To get a good result in Resolve, think of how you would get a good Result in Photoshop.
You would skew the image you're trying to insert to match the
perspective of the Television's frame.
You would feather the edges of the selection to match the camera's
You would use an additive blending mode, so that it look like the TV
was emitting light, and you would balance the contribution of the
glare on the front of the TV, depending on how bright you wanted it
You might add "spill" as if the TV were adding light to the room
(maybe not in this case, because the room is bright).
But with a moving image, especially if the camera is moving, you also need to "matchmove" or "cornerpin" the image you're inserting, so that it appears locked to the screen.
For the sake of simplicity, lets say that your camera is still and you don't need to track, matchmove, or cornerpin. If that's the case, then 99% of what you need to do can be accomplished in the inspector panel of Resolve's Edit Page. There are alternative methods for both the Fusion and Color pages, but the Edit Page is the most straightforward for simple tasks. The process would go something like this:
Import both pieces of your footage into the media pool (cmd/ctrl-I)
Drag the background image (livingroom scene) onto V1 on your
timeline. Drag the foreground image onto V2. Think of the vertical
stack of timeline layers in Resolve like Photoshop's layers. Like
Photoshop, Resolve "sees" the stack from the top down.
Adjust the size, position, and perspective of the foreground layer to
match the perspective of the TV frame. In Resolve, select the
foreground "V2" clip, open the inspector panel, and adjust the zoom,
position, rotation, pan, and tilt attributes until your image lines
up. You can also crop the image a tiny amount, and use the "soft"
slider in lieu of Photoshop's "feathering" controls.
Adjust the composite blend mode in the inspector. "Add" or "Screen"
are usually good for this type of additive, emissive light. Adjust
the "opacity" slider to taste.
You can also add effects, similar to Photoshop plugins, by dragging
one from the "effect" tab onto either clip in the timeline. You
could, for example add a slight glow to V2's clip to help sell the composite.
Controls for these effects will appear in a new tab of the inspector
once you've applied one (the specifics of this tab's placement depend
on which version of Resolve you're using.)