How to implement NFC payments?

You won't be able to support NFC payment in your application, unless you are a bank with a Visa/Mastercard/etc agreement, and have access to a certificate to sign your EMV transactions.

Contactless EMV transactions are not encrypted. That is why you can easily sniff a contactless transaction, or read a contactless payment card info.

Transactions are still secured because of a certificate embedded in the card, specific to the card issuer (ex : Visa, mastercard). This certificate is protected (can't be read). It is used to sign the transaction details (amount, date, random identifier, etc.), so that the POS and transaction processor (on the bank side) can authenticate and validate the transaction. Without a valid signature, your transaction will be rejected.

However, since all major card issuers added mobile payment support to their latest specification (ex : mastercard PayPass 3.0, Visa PayWave 2.1). They may eventually offer API for other apps on the phone to initiate tranasctions.Still, my understanding is that phones will need some specific hardware (ex : a cryptoprocessor) to process transactions.

A starting point for reading would be "Host Based Card Emulation"

https://en.wikipedia.org/wiki/Host_card_emulation

https://developer.android.com/guide/topics/connectivity/nfc/hce.html