Typically this utilised a negative photographic plate (so that bright objects appeared as dark against a light background making their presence easier to detect for our visual system), and the plates were rapidly flipped. The object which moved or suddenly appeared and disappeared was the new element.
This works for nearby moving objects (planets, asteroids, comets) which would track against the stellar background, or distant variable ones (supernovae, variable stars, pulsars) which would appear and disappear (or brighten and fade) over time.
Now of course this is automated and direct sensor readings can be interpreted, but the childs' game was at one time Best Scientific Practice.
Described here, "How are asteroids discovered?" https://catalina.lpl.arizona.edu/faq/how-are-asteroids-disco...>.
There are archives of these astronomical plates, and there are projects which utilise older observations so recorded to make new discoveries even now (or in the recent past). I'd first learned of this visiting the Lick Observatory on Mt. Hamilton near San Jose some years back. Key was that old plates were used to compare current observations using the same 'scope, an otherwise now-archaic instrument but not without its advantages. As I recall, the astronomer doing the study was the same one who'd made the original plates many decades earlier, and was doing this as his own retirement project. There's a description of similar work (including Lick observations) here:
"Astronomy's Photographic Glass Plates: Demonstrating Value Through Use Cases"
https://journals.library.ualberta.ca/istl/index.php/istl/art...>
On plate archives:
"Preserving an Astronomical Legacy"
https://skyandtelescope.org/astronomy-news/preserving-an-ast...>
"APPLAUSE: Archives of Photographic PLates for Astronomical USE"
https://www.plate-archive.org/applause/info/>
(dylan604 noted this use case earlier: https://news.ycombinator.com/item?id=42657956>)