Edit - As @Developer Wonk pointed out in a comment, Checkfront have a specific Salesforce integration. You can find step-by-step installation instructions on their site:
The Salesforce add-on provides the ability to automatically create new
customers (or update existing ones) in Salesforce when a booking is
created via Checkfront.
This will ensure your customer records are kept in sync, and you can
take full advantage of the many advanced customer management tools
Salesforce has to offer.
When enabled, a new account is created in Salesforce after a booking
is made. A personal contact is created under the account, along with
an event that is tied to the booking date and details. You can further
customize this in your Checkfront setup. Please note, an email or
phone number must be supplied to create or update the account.
Setup is quick and easy and requires the installation of a Checkfront
package in Salesforce. Follow the instructions below to find out how
to do this and get your integration up and running in no time!
To enable the Salesforce extension, navigate to Manage > Add-ons in
your Checkfront dashboard and click on Setup in the Salesforce tile.
Before clicking on the activate button, you must first click Install
the Checkfront Salesforce Package link. This will take you into your
Salesforce account where you can proceed to install the Checkfront
Click the Continue button to move on to the next step.
Next, you must approve the package API access. Simply click Next to
In step 2, you’ll see the view above. Click Install to continue with
the package installation. The system will now proceed to install the
You can now go ahead and complete the activation in Checkfront.
Check the boxes to allow Checkfront to create accounts, contacts and
events in Salesforce, then click Activate.
Salesforce will now display a message to let you know that Checkfront is requesting permission to access your basic information and manage data on your behalf. Click the Allow button.
Setup is now complete!
I've just taken a quick look at the Checkfront Webhook docs and it doesn't look like they support outbound authentication, only inbound authentication. I believe the details you have - the Consumer Key and Secret, etc - are likely for inbound authentications to Checkfront, not outbound authentications to e.g. Salesforce.
If you aren't able to make authenticated outbound requests, you could make unauthenticated requests - see this article for an explanation. This could pose a security risk, however.
Alternatively, instead of having Checkfront push to Salesforce, you could set Salesforce up to periodically authenticate with Checkfront and check for new records to pull. This won't be real-time, but it will be secure. In that case, you'd store the credentials you posted above as a Named Credential in Salesforce and make callouts that way. This post provides a good overview of Named Credentials and how to use them.