How do you get common debris?

Yes "Common Debris" are obtained from slavaging white items and you can drop it on monsters too.

I played 1-2 hours (in Torment 1) yesterday, I've looted ~30 white items and some Common Debris.

Paf's answer is right about how to get it - salvage white items, or count for drops from monsters. I'd like to add my suggestion for the most efficient way to get it: start a new character, or play Act I on lowest difficulty with a character with low or none magic find bonus . It seems the debris can be salvaged from any white item, and the most I've seen was at the start of the game.

Fastest way is to make a new char (barb) over and over and scavenge the starting items.