Other replies covered chip timing, but, if a race isn’t using chip timing, the usual way to do it is to have a timekeeper (or several, for redundancy) taking a time each time a runner crosses the line; after crossing the line, the runners are herded into a funnel and need to stay in order until they walk by someone at the other end of the funnel who notes down their number. Then, after the race, the list of times and the list of race numbers are correlated - if things have gone right, there are the same number of each and it’s easy, but even if things haven’t gone right you can usually patch up the results. Doing this two-step dance means that there’s no queue as you cross the finish line, since pressing the lap button on a stopwatch is really quick.
Other replies covered chip timing, but, if a race isn’t using chip timing, the usual way to do it is to have a timekeeper (or several, for redundancy) taking a time each time a runner crosses the line; after crossing the line, the runners are herded into a funnel and need to stay in order until they walk by someone at the other end of the funnel who notes down their number. Then, after the race, the list of times and the list of race numbers are correlated - if things have gone right, there are the same number of each and it’s easy, but even if things haven’t gone right you can usually patch up the results. Doing this two-step dance means that there’s no queue as you cross the finish line, since pressing the lap button on a stopwatch is really quick.