Mike Hayes shares about real live connections that people are making with him. He explains how to use customized connection requests to improve the odds of getting a good response. 

After the connection is made then ask for a simple action step tp start building trust.

Finally, the follow up or lack of follow up will either build up the relationship or tear it down.

So to build you relationships, use LinkedIn's "customized connection requests" and then build trust with small action steps and follow up!