In after effects create a new composition to the size you want your video either 1920X1080 or 1280 x 720 for youtube HD
with a black background
create a new solid layer that fits to comp and is white
Go to effect > noise & Grain > Fractal Noise
untick uniform scale check box
and adjust the scale width so it stretches across the screen so move slider to right
adjust scale height so you get thin lines so move slider to left
then go back to top to adjust the contrast depending on if you want it darker or lighter the higher the contrast the more black and white it will be the lower the contrast the more grey it will be.
Now holding down alt Key on your keyboard click the stop watch for keyreames in Evolution box this will bring up the wiggle expression in the timeline.
delete what is there and type time*1000 and press enter this will animate the noise randomly
Now create a new solid layer, make comp size, white, go to effects> noise and grain> fractal noise
keep uniform scaling box checked this time and move slider to left so you get small dots
Alt + click the evolution stopwatch again wiggle expression same as before time*1000
and adjust contrast to suit
In the layer panel change this layer blending mode to multiply or add depending if you want dark or brighter and then tweak the contrast on both layers for final results.
press play to make sure you have a semi realistic static effect
add your logo and animate as you see fit