Networking is about building relationships with people. It's as simple as making friends with someone.

Would you ever approach a stranger and ask her point-blank, “Please could you help find me an opportunity?” They would probably be repelled by such an approach and walk away. However, you could make that request to someone who you already know.

If you're approaching someone on LinkedIn whom you don't know, you have to first break the ice – perhaps request to take them out for a coffee/lunch and find something familiar to talk about. You will figure out whether you're able to build a rapport in that meeting. You're not meant to get along with everyone, so if it's not going in your way, don't fret.

If you're not in the same city, you could request for some time over a call (see point 7 on how to make this request).