Generally speaking, the task of authorizing a user to a client of protected resources through OAuth 2.0 is not too trivial and is hardly needed on a simple landing page.
I am familiar with the methods of working with OAuth in java and, since you did not specify the required toolkit, I will give an example of the implementation of OAuth authorization on it.
For authorization, you will need a client that implements Authorization Code Flow (for more information about it, see RFC6749) For applications on java, this will be Spring Security OAuth or Apache Oltu. For applications in other languages you can find a suitable client here . After that, in accordance with Authorization Code Flow, you will need to obtain user authorization to access its resource (here you must specify the necessary scope, in this case it will be r_fullprofile). After that, you will get an Auth code, exchange it for an access token, and request the people point (it is in the documentation, there is not enough reputation link :)). From there, user information will come to you.
An example of a similar interaction with Google+ can be found here: OAuth_QrealWeb
The specified project is quite large, you will be interested in the OAuth2Config package.
The comments have already indicated a link to the LinkedIn API, where you will find all the necessary information about access points and connection methods.
In order to provide a more complete answer, you need to know at least the tools used.