Firstly to get your QR Code or Public Key have a look at http://help.trustology.io/articles/2774442-what-is-a-qr-code-and-what-is-it-for
Then follow the instructions for the source you are receiving from?
A record of a new payment will appear in the Account Details screen.
Transactions you have created will show up in your transaction history almost instantly as "pending transactions". Once the transaction has been confirmed it will be displayed as a valid transaction. Same with incoming transactions, they will show up once confirmed by the blockchain network.
Tap on a transaction and you’ll open the "Transaction Details" screen giving you more details such as the time it arrived and the transaction costs. There’s also an option at the bottom of the screen to view transaction on a block explorer.
The amount of time it takes for a transaction to be confirmed is dependant on the blockchain and cannot be influenced by TrustVault. At the time of writing it takes usually around one minute.