Embedding another video to "blend" with the environment
If you can use a tool like Apple's Motion or FCPX, or Adobe's After Effects, they all have the ability to put the 4 corners of a layer anywhere you want. With Motion or After Effects, you can even track the 4 corners and keep the "TV" image pinned in the right place.

In Motion, you can select a clip and open the Inspector. In the Inspector, press the "Properties" tab. There's a section in the properties called "Four Corner". If you twirl that open, it allows you to set where the 4 corners of the video go. You can put them wherever you like.

FCPX is similar - select the clip, and open the inspector. There should be a section in the inspector named "Distort". This will also let you set the 4 corners of the clip.

In After Effects you can select a layer and apply the built-in "Corner Pin" effect.