First, you'll need to go to Settings > General > Siri and check that Siri is turned on. Then, you should turn on Allow "Hey Siri," which will then bring up the setup menu for the virtual assistant.
Follow the on-screen prompts to train Siri to recognise your voice. Make sure you speak as naturally as you can, because this is the voice and sound that your phone will be listening out for from now on.
It'll ask you to say "Hey Siri" a few times, and then sentences such as "Hey Siri, how's the weather today?" and "Hey Siri, it's me."
Once you've finished the Set Up process you're ready to go. On older iPhones, you'll only be able to use Hey Siri when you're connected to a power source, but with the iPhone 6s and iPhone 6s Plus, you can use it any time.
There's loads more that Siri can do in iOS 9, and we're working on updating this article to explore its new features, but the main one is Proactive, which you can read all about in our article on How to use Proactive in iOS 9.
Note: The rest of this article was written prior to September's release of iOS 9. We're working on updating this article so check back regularly for new updates, and read on for all of the information we had ahead of its release (much of which still applies!)
Siri also powers the new Proactive assistance feature in iOS 9, which is Apple's answer to Google Now. It can take into account your location, the time of day, reaccuring activity, usage patterns, the app you are viewing or other connected devices to anticipate your next move and surface relevant actions and information, before you even have the chance to ask a question or type in a query.
In iOS 9, you'll be able to ask Siri to "remind me about this when I get home," when you're on a particular web page that you want to come back later, for example.
Some of the question examples Apple gives include: "Show me videos I took at Iva's birthday party," "Show me photos rom Utah last August," and "Remind me about this when I get to my car."
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