On the battle map a hero can move a number of tiles equal to their speed (round down) per action point. When the hero is selected, tiles they can move to without using all their available AP are highlighted in green. Moving to a yellow-highlighted tile will end their turn. (Abilities like Heroism can let a hero start their turn with more than 2 AP.)
Diagonals cost 1.41 movement points. Passing through a tile that is already occupied by an ally costs an extra 0.5 movement point. Hazards such as Gorgon Corrupted Land also cost +0.5 movement point.
Monster movement ranges can be seen by hovering over the monster portrait in the top right of the UI.
Groups that start together and are moving to the same destination or task will stay together, moving at the speed of the slowest member. So for quick jobs, adding a slow hero to the task sometimes can make the whole thing take longer to finish, by delaying when work begins.
If more than one group of heroes is moving to work on a job, work will begin as soon as the first group of heroes arrives, and in some cases might be completed before a distant group has even arrived. The exception is Assault missions, which will wait until everyone has arrived.