So, the white piece has identification, but the front cover does not. How are these identified? It's from an old space set from the 90's. I have tons of non typical parts that seem to have no identification. It does have some numbers on it - 1-02 what is that referencing? I know this was from a few sets, probably
The box is part 4345 (or a variant). On BrickLink, that gives This Door, Frame fits with the following Door:. And those parts are 4346. But you want one with a pattern on it, so the BrickLink search you need is 4346p*. There's only 60 of them, and one looks right: 4346pb05 Container, Box 2 x 2 x 2 Door with Slot with Red and Yellow Controls Pattern
As for "1-02 what is that referencing" it is almost definitely a way for Lego to track which part of which mold made that part, so that if any are reported as mis-formed, they can track it down more easily.
Note the similarity to this part (below). You can see the left side is different.
As for finding pieces yourself, I find the Bricklink search to be most useful. Obviously as you become more familiar it will be easier. Searching by colour is usually a good way to start.