First, create a watch for each participant in each race (see How Do I Add People to a Race?).Then to launch the race, you can use the following features.
If Staggered Start is turned on in the Settings, each watch is launched X seconds after the previous watch. It also puts the person's name and their countdown in huge letters so you can simply show the participants the screen. (But, note you can shrink the launcher if you want to see the watches during the start.)
Big Start ButtonIn Settings, you can also choose to have a very large Start button at the top of screen. Depending on whether you're already started the race and whether you're using Staggered Start, the button will vary between "All Start", "Staggered Start", "All Stop", or if a race is going and you've added any new watches, "New Watch Start", or "Stagger New Watches". After you've started, the button will shrink, allowing either "All Stop" or "Cancel Staggered Start".
Volume ControlIn order to avoid having to look at the screen, you can also use your phone or tablet's physical volume button. At the beginning and nobody's running, or you've added runners, to launch the race, just press either Volume Up or Down. After the race is going, the Up bottom means Lap, and the Down volume button means Stop.
If you have only one watch running, then that Lap or Stop naturally applies to that watch.
BUT if you have multiple watches going, then Watches will create a temporary Lap or Stop button that you can either drag to, or tap to select, the appropriate person. So if you have two people crossing at the same moment, you can just create two Laps and then drag them when you have time.