To launch Siri, hold down the home button for a few seconds. After the double-beep, state your request. You can tell that Siri is waiting for a response if there is purple light in the microphone.
You can tap the "i" on the right to get a menu showing different things you can ask Siri.
You can also ask Siri "What can I say?" at any time to get this menu.
Another option is to enable "Raise to Speak" to allow putting the iPhone to your ear (like taking a phone call) to activate Siri.