Azure

Download and install Postman
Click Here to download the Azure Postman collection
Make sure you are in the "Azure REST" environment, then select "Manage Environment" with the settings cog
Set your environment variables in the "Current Value" column:
Variables:
1. tenantId: Azure Dashboard > Azure Active Directory > Manage/Properties > Copy "Directory ID"
2. clientId: Azure Dashboard > Azure Active Directory > App Registrations > Select/Create > Copy "Application ID"
3. clientSecret: Select App Registration > Settings > Keys > Create new "Passwords" > Copy Secret Key "Value"
4. subscriptionId: Azure Dashboard > Subscriptions > Select > Overview > Copy "Subscription ID"
5. action: API call that you wish to make (e.g: resourceGroups?api-version=2014-04-01)
If done correctly, you should be able to execute the "Get AAD Token" step in order to obtain the Bearer token for authentication for API calls. You can now execute the "Azure REST API Request" action and receive a response from Azure
Note that some modifications may be necessary (such as the HTTP action or the URL) in order to make specific API requests. You can defer to the "Azure Resource Explorer" (link in Additional Info) for further details on how the API call should be formatted.

AWS

Download and install Postman
Click Here to download the AWS Postman collection
Make sure you are in the "AWS REST" environment, then select "Manage Environment" with the Settings cog
Set your environment variables in the "Current Value" column
Variables
1. accessKey: Programmatic API access key from configured IAM user
2. secretKey: Programmatic API secret key from configured IAM user
3. contentType: Generic JSON format since Postman's default value will cause errors
4. service: Name of the AWS API service you're attempting to query
5. region: Optional. Specific region for the query, if desired
6. version: Enforce versioning for V4 signing protocol, which is what Postman will be using for authentication
7. action: API call you're wanting to make
If done correctly, after filling out these variables you should be able to get a response by clicking "Send"
Note that you may need to change the HTTP request type (GET, POST, PUT) depending on the desired API call. You may also need to modify the URL to accommodate additional requirements depending on the API call (e.g: Buckets for S3 requests). You can reference the API guides in Additional Information for more details on how the API call should be formatted.

Azure Resource Explorer (See the REST API responses made from/by Azure, better understanding of proper query format)