LinkedIn is a great way to expand your network or find key people at a company. If you don't have a shared contact with someone on LinkedIn, however, you can't view that person's full contact information. Here is how to work around the limitation without paying for LinkedIn Premium.
First, find out as much as you can about the person you are searching for (like their job title and employer) while logged into LinkedIn. Using a different browser, search for this person on Google, using the information LinkedIn provided. Often, the person's full LinkedIn public profile will show up in the Google search results instead of the limited profile you'd get as a LinkedIn Free member.
This loophole could be fixed by LinkedIn in the future and only works with public profiles, so your mileage may vary.
Legally View Public Information For A 3rd Degree Connection On LinkedIn | AddictiveTips