You mean like recently here in metro Buffalo?

Snowplows (mounted on dump trucks) push the snow to the sides of the road. Front-loaders scoop up snow and either put it into dump trucks or dump it on the side of the road. In situations like this past storm, add in tow trucks and forklifts moving cars that were stuck in the road and abandoned, but that's not usually needed.

As for digging out at home, if you can open your door, then you start digging there. Remember to throw the snow up and over the snow blocking the exit. If you can't open your door, maybe you can open a different door or go out a window. Worst case, you gotta hope you have a friendly neighbor who can help you get free.