Log in PayPal developer account at https://developer.paypal.com using your usual PayPal login credentials.
Go to 'My Apps and Credentials' and click 'Create app':
Add App name and select your Sandbox developer account (if you don't have any, you need to create it: Sandbox -> Accounts.
Read more about sandbox accounts in PayPal Sandbox Testing Guide.
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:
If you have any questions regarding PayPal sandbox settings, your account restrictions or settings please contact PayPal support.