I will need more details on what you are trying to do. The answer is easy, if the person whose profile data has to be extracted is aware, then you can create a Linkedin application by using http://developer.linkedin.com/
You can store the user profile and all the variables you need directly into a database.
However, if becomes far tricky if you want to extract information of users without their awareness. In this case, you will need to first find a way to open all profiles as Linkedin would not allow you to open 3rd degree connections profiles directly and then write a HTML scrapper to pull out information. You can look at tools like import.io or Python libraries like Beautiful Soup to do this.
I would personally recommend the first option over other, as creating second will take lot more time and you will need to change the algorithm every time Linkedin makes changes in the way pages are displayed.
Hope this helps.