Ways to access Apple Pay
Some ways are:

From the lock screen - Go to Settings -> Wallet &amp; Apple Pay and enable Double-Click Home Button. Now when you double-click on the lock screen your cards will appear. Then select your card and use Touch ID or hold it next to the reader. One of the quickest and easiest ways.

Siri - You can access Apple Pay by saying "Apple Pay" to Siri.

Wallet App - Go to the wallet.app, click on your card at the top. Then when you rest your finger on the home button, it will authenticate it and search for a nearby reader.

Holding it near the reader - When you hold your iPhone near a card reader it will automatically bring up your list of cards.

You might also want to check out Apple Pay.