Perennials: A quick watering (around 10-20secs) every day or every other day. These will show signs of drooping and shriveling if not getting enough water. You can cut down to once or twice a week probably after 2 weeks of watering. This will reflect how hot it is though. There's no perfect formula for when to stop watering. If they look sick, water them at the base of root ball. Since annuals dry up faster, it is important to water them daily for best results.
Important: Signs of over-watering can be yellow leaves appearing. Also, if the plants look like they are dying but you know you are watering them enough, then you may be watering them too much, too frequently. And signs of dehydrated plants are shriveled, wrinkled, curled up leaves. Look at them now while they are healthy so you know what normal leaves look like. Regarding rain: unless it was a steady rainfall for 4-5hours, then the plants need watered (maybe not as much) but still needs watering. Unfortunately a quick heavy rainfall will not sink into the root ball far enough, if at all because the mulch and leaves will also stop the water from reaching the root ball too, so keep that in mind.