Not sure if you are asking about the computer in your example or the logos.
A lot of drawings like these are made by drawing over a picture or using
trace option in illustrator.
- Take an image into illustrator and play with trace.
- Or, take it into illustrator, make a new layer, lock the layer with
the image, and trace by hand the lines you need.
This process would be easiest if you have made the image black and white with high contrast in photoshop first. Here is a post explaining these approaches.
Generally, the most efficient way is to sketch lots of ideas on paper. And in the case of LinkedIn and Facebook, slight alteration of an existing font (this usually done in illustrator by writing text - > create outline - > ungroup - > alter the vector bezier points to your hearts content).
Using some kind of animation programme (such as flash, Blender, GoAnimate, AnimeStudio, or a bunch of others, depending on your preferences and what the end goal is).