Which also makes me wonder how many of the shooting stars I've seen recently are just old starlinks burning up.
2. The sky needs to be dark enough to see it (so twilight or night)
3. The satellite needs to be illuminated by the sun.
4. The satellite needs to reflect enough light that you can see it.
Basically this happens just before sunrise, and just after sunset. So the ground and sky are dark (allowing you to see through the atmosphere), and the satellite - being at high altitude - is still illuminated.
As they pass overhead, you can often see them suddenly vanish as they pass into the Earth's shadow.
The International Space Station is a good one to find, as it's quite bright (very large).
There are various websites and apps; some phone apps use the GPS and magnetometer to show you what direction and time to look, and a search tool to look for visible objects at your location. It used to be really good with the old Iridium satellites, which gave a bright flash due to their large flat antennas.
I've seen plenty of satellites in the middle of the night, from very dark areas (wilderness). They look like stars, only they move more quickly. These observations go back a decade, at least.
I can tell you that they look like stars - so much that I need a reference point, an actual star or planet, to verify they are moving and not a 'stationary' star (judging movement being otherwise very difficult at that distance). They move very steadily, horizon to horizon, or as far as I can track them. A wild guess, based on memory, is one might take 5 or 10 minutes to cross between my horizons (usually I'm not on a plain - trees, hills, mountains may elevate my 'horizons' and reduce the distance).
Natural celestial object? No way a star is moving that fast relative to other stars and Earth's horizons. Asteroid? That seems hard to believe, due to size and illumination. Comet? Are there lots of tiny ones? I never see tails. Maybe a meteorite entering the atmosphere that doesn't yet have a tail?
Other human-made objects? Airplanes would look bigger and have colored, blinking lights - I've seen plenty of airplanes at night. Maybe there are higher flying airplanes without the colored and blinking lights? Are they illuminated whitish, and so far away they'd look like stars?
I've seen them so many times, I'm confident that I could take anyone to a wilderness area on a clear night and find one within 15-20 minutes, probably less.
And the distance - most asteroids pass by much further out than even the moon, so their motion would be hard to detect.