How to use Apple Pay Cash
To send or request money, tap the iMessage app like you would to text the contact in question and select the Apple Pay icon from the app drawer at the bottom. This will populate the text screen with a keypad and a "Send" and "Request" button to alert your debtor/payee that you just paid them or that they are on the hook for a certain sum. Incoming transactions are automatically accepted and instantly available on your APC card (which you can use to make actual purchases online or deposit into your real-life bank account). If your hands are full, you can also just ask Siri to send a payment to one of your trusted contacts, and she'll make it happen.
Unfortunately for Android users, this is an iOS-exclusive feature. And even if you have APC set up on your iPhone and want to send your fellow iPhone-owning friend some cash for covering the bar tab last night, they must have APC set up as well (you'll get a notice if they don't before you're allowed to send or request any funds).