To create a LinkedIn App, go and visit: https://www.linkedin.com/secure/developer.
You need to be logged in to your LinkedIn account to be able to access their developer page. So first, login to your LinkedIn account and then follow the link above to get to their developer page. This should look similar to the one shown in the image below:
Within the Application Info make sure, that you enter the correct URL of your website and that the URL you enter there does match 100% the one from your website. So if the URL of your website does include the www like http://www.domain.com than you need to enter it like that. If the URL of your website doesn't include the www, than you don't need to include the www within the URL. It's important that the entered Website URL does match the one from your actual website, otherwise the App won't work correctly and it will show an error message when you or your users try to connect with the App.
After you added the application you will see a app listing page which will contain all the needed information to integrate that App in to your website. See image below:
Use the "OAuth 2.0 Redirect URLs" field same as the LinkedIn callback url. If these entries do not completely match the URL of your website, the application won't work and it will show an error message whe you try to connect to the App.
Important: When you copy and paste all the needed IDs and Keys, make sure, that you don't have any empty spaces, either at the beginning nor at the end of these entries. If you have any empty spaces, then the Application won't work and will show an error message when you try to connect to the App.
After you entered the App ID and App Secret, click on the "Save Changes" button within the plugin's settings page.