I always start with building rapport first. Keep it light, no politics, and be careful even about sports. There is a reason "How about that weather" is a cliche, it works! If you know anything about the person you are calling, make sure to reference it. Give out semi personal information to build the relationship. My wife was dog-walker for a few years, and I would always reference that when talking about the weather. Then we would talk about their pets. People will talk about their pets with strangers, but children might get a little too personal.
Your should never try to close on your first call. Use it only to set up a meeting later on. The meeting could even be the same day, but letting them off the hook from the get go helps them trust you more. Starting off with
You don't have time now to talk right? How would this afternoon or tomorrow morning be better for you?
I always tried to give the prospect as many "outs" as possible. I would say things like "Oh well you probably don't have any problems with [common problem] do you?" Most will be honest if you have good rapport. Once you find the issue they are having, focus on it, and explore the issues they are facing, solutions they have tried, and what they are trying currently. Don't even mention your service until you have a good grasp on where they are now. Listen more than you talk.
IF at any time, you feel like you just aren't clicking with a prospect, say
"Hey, you know, my [supervisor/copywriter/editor/manager] is right here, you wouldn't have a second to introduce yourself to him, would you?"
Having a second person take over a call can change a prospects view. Personalities don't always click, you may have said something totally innocuous that just didn't sit well. A different person might do the trick. Plus this wording strokes the prospects ego a bit.
I would reccomend looking up the "Sandler Training" or downloading some sales cds. Some of the techniques seem over the top, and they are, but they will give you confidence and skills to cold call effectively.