When someone submits a form and payment

When someone submits a form and payment how do I know if they have paid or not?

You should get a notification from your Payment processor (ie. Paypal, Authroize.net, etc.) if they completed the payment.

if the user changed her mind in the last minute, you should see  incomplete payments in the submissions view section. That means the user did not submit the payment.

See this guide Setting Up Email Notifications