There is no one size fits all approach in this regard and part of it has to do with the brand you have already developed for yourself. I have mentored startups and people looking to get into broader networks and from personal experience as previous experts have noted, you have to show interest in them and explain why there is value in connecting with you. I would first find the LinkedIN groups they are part of in which you share a common interest. Start populating into those group with relevant content or commentary. This way it will not be a "cold call" as they may have read or at least seen your name pass by their screen. This also works in Twitter where you can follow them and post content or reply intelligently to tweets they post. Offline you can attend presentations, meetups and/or conferences in the same area to meet with 2nd connections who could also introduce you. The other common method is via referral if you have a connection through a colleague or friend.