Log in PayPal developer account at https://developer.paypal.com using your usual PayPal login credentials.
Go to 'My Apps and Credentials' and select 'Live' (live keys) or 'Sandbox' (test keys for demo mode):
'Add App name (it could be anything: e.g. your site name or business name) and click 'Create App:
Please remember that PayPal has its own restrictions for accounts from different countries. Sometimes you need to have business account (e.g. Russia), sometimes personal is enough (e.g. USA).
Once you've created an app, you can either enable testing mode or live mode.
Copy your 'Live' API credentials and paste them in your WP admin area.
Disable Demo mode when you are ready to accept payments in Live mode.
PayPal smart Buttons
Activating the option PayPal smart Buttons will give your clients an opportunity to pay with their credit cards even if they don't have a PayPal account.
PLEASE NOTE! this option is available only for customers from the United States of America, Canada, and the United Kingdom.
Option 'Hide checkout fields' allows your customers to skip ordinary checkout and pay with their PayPal account / Debit or Credit Card in just 1 click (works only when PayPal smart Buttons are enabled in your WordPress admin area).
But remember that other payment methods except PayPal will be unavailable if the option 'Hide checkout fields' is enabled. This option is strongly recommended if you have PayPal as your only one single payment gateway.
If you have any questions regarding PayPal sandbox settings, your account restrictions or settings please contact PayPal support.