To start a timer, just tap the clock icon on the timer. Tap the clock icon again to stop it. If a timer is running, you can switch timers by just tapping on the clock icon for a different timer (no need to stop the first timer).

A running timer will keep running when you close Hours.

You can also start and stop your most recent timers from the notification widget. See the FAQ on the widget to learn how to set that up.