It's just like using a contactless payment card (such as Oyster). You'll need to touch in and out on tube and rail services, but on trams and buses, you'll only need to touch in. You should use the same device for your travel, so you can benefit from fare-capping and avoid incomplete journeys. And don't forget to keep contactless cards separate from your device, and make sure you have enough battery life to complete your journey.
Touching in and out with your iPhone
Open Passbook or Wallet and place your finger on the Touch ID button. Within 60 seconds, you'll need to touch your iPhone on the yellow card reader, making sure the top of your phone is flat against it. As soon as your payment is complete, a green light will show on the card reader. Your phone will gently pulse (and beep) and you'll see a tick on your phone display.
Touching in and out with your Apple Watch
Start by double clicking the side button. Within 60 seconds, you'll need to touch the face of the watch on the yellow card reader. A green light will show and a subtle pulse and beep from your watch will let you know your payment has taken place.