Usually a hero takes 3 seconds to make its next move, after its current move has ended. When the hero is slowed, it takes an extra 1 seconds to make its next move.
The slow effect lasts for 4 seconds in total, which is the sum of the normal 3 seconds (for one move) and the extra 1 second (of slow). If slows triggers in between two moves, the slow effect is shared between two turns, but have the same overall effect.
Slow is applied when a blue 'SPD DOWN' appears.
This is tested with Achilles' tremor and Atalanta's chilling shot. A video was taken and watched in slow motion to measure the timings. More information is still needed on how it affects ultimate skills and walking speed.
(Need help to test that this is correct for different heroes and cases)
Heroes that can slow: