To use such an API, simply register your APP on Linkedin Developers and create a script that performs http requests to get website data (More details in the documentation itself).
Fortunately, there is a python module that works as an abstraction layer, which allows us to save time by avoiding codifying the request scripts again. The name of the module is python-Linkedin, and is available for download via Pip.
#Example of official documentation
from linkedin import linkedin
API_KEY = "wFNJekVpDCJtRPFX812pQsJee-gt0zO4X5XmG6wcfSOSlLocxodAXNMbl0_hw3Vl"
API_SECRET = "daJDa6_8UcnGMw1yuq9TjoO_PMKukXMo8vEMo7Qv5J-G3SPgrAV0FqFCd0TNjQyG"
RETURN_URL = "http://localhost:8000"
authentication = linkedin.LinkedInAuthentication(API_KEY, API_SECRET, RETURN_URL, linkedin.PERMISSIONS.enums.values())
print(authentication.authorization_url)
application = linkedin.LinkedInApplication(authentication)
The values that must go in the variables API_SECRET and API_KEY are informed to you once you register your APP (They are unique values and should be used only by you in a specific project).