To set up online payments using Braintree, follow these steps:
Log in to https://www.braintreepayments.com/ .
Click Account and select My user.
In the Authorization section, click API Keys.
On this page, you’ll need to copy the Public Key, Private Key, and the Merchant ID.
In BookingBug, click the Cog/Settings icon > Advanced Settings > Configure Online Payments.
Select Braintree as your payment provider, and enter the details copied in the previous step.
Configure your other settings such as requiring payment to book, sending cancellation emails, etc.
Please note, if you would like to make some test payments (not involving money) you'll need a Braintree Sandbox account and use test values as oppose to real card numbers. You can read more about Sandbox here.