Research
Here's some links to my Pinterest Boards:
GIFs
My quick initial test GIF in Photoshop!
Two GIFs made for the GIF class assignment
Here's how I did it!
For the television, I had constructed the physical elements of the TV set in Photoshop, like the knobs and the screen, using shape, patterns, gradients, and blending effects.
I used a mask on the screen to make it easy to drop in images and make them fit the shape of the screen.  I used pictures that I had taken and pixelated them a bit. For the static, I used a couple blank layers that had a mezzotint filter effect, and cycled through them for a few frames between the images to create the channel-changing effect. The blank TV asset:
I then updated the LA GIF to involve more motion.
For this, I created a circle with a warm gradient to make the sun and used wave effects to add motion to it, and created a cool-colored background to contrast it.
To create the motion, I took the building and cloud assets and duplicated them.  The first set of buildings and clouds start on the screen and move off to the left. The second set of images starts off the screen to the right and moves onto the screen and loops from there, creating a seamless loop.  The clouds move a bit slower than the buildings, creating a slight parallax effect. 
The LA text cycles through 17 different fonts. The entire GIF is 400 frames.
Inspirations from Pinterest:
Cinemagraphs
My initial test cinemagraph! I used my phone to record a simple video with simple motions.
The Photoshop Timeline for this GIF
The Photoshop Timeline for this GIF
Here is a higher quality cinemagraph, I used another DSLR camera to film it.  I wanted to do something that represents me and my love for photography.  I had planned out the composition of this piece, and split the three different motions into the thirds of the composition.
As you can see by the Photoshop timeline, I had a base frame from the video, and overlayed the different motions separately from each other. By having each motion be separated, I can place them in the sequence how I want.  The eye-blink motion was originally right before the finger movement, but I wanted the GIF to be longer, so I spaced the motions out so that there is not overwhelming motion all at once. Using small fade transitions also helped the movement flow and morph better into/out of the base frame.
This Cinemagraph was much more difficult to get to loop seamlessly.  As you can see by the timeline below, I needed to use more layers. Originally, the hands would visibly shift to the right when looping. To fix this, I duplicated the layer at the end of the timeline, shifted it over a few pixels, and did that twice. That makes it so by the end of the GIF, the hands are shifted back into a position that looks almost identical as the beginning, allowing it to loop.  The head movement was very basic and didn't require much altering.
The GIF is long; about 450 frames. That makes it harder to notice any clipping that occurs when looping