Largely it's down to doing the same things that make you a good communicator in general. A couple of very simple examples:
Sit upright when you call and smile. You want to be relaxed but alert (sitting upright) so you breath calmly and have plenty of energy behind your voice. And smiling when talking changes the entire character of your voice. Make an exaggerated smile - in general people come across as smiling less than they think they do, and this is even more the case over the phone. It really does come across as much friendlier and relaxed. Try it and record your voice with and without a smile.
And listen to any cue you get about their business and parrot it back to them either as statements or questions. "So you feel your payment provider don't understand your side of the story?". The more they talk, the more likely they are to talk themselves into buying your product, because the more people get to talk about themselves with only small interjections that shows you've listened to what they say, the more they feel you understand them.
If they start talking a lot, you often only need to very subtly tie that to your own experience (creating shared experiences creates a connection) related to providing your product or services. E.g. "I feel the same way - when I started building X, it was because I'd done Y in a previous job and I kept running into the same problems; once we ...; I think we have a good solution, but how are you solving that for your business?"
Generally, I'd say a foundation to get comfortable with this for someone who is uncomfortable selling, is not a sales book or course, but a conversational skills book. Look up Leil Lowndes - she has a lot of easily digested conversational skills books and most of the skills are directly transferable to making your more comfortable with sales. And especially if you're selling your own product that you can muster excitement about, coming across as confident and a good conversationalist brings you 90% of the way there. Get that in place and you can top it up with some general sales skills later.
_Your_ ability will show, or won't, in the general knowledge and individual focus of your questions. If you can't ask good questions, you aren't ready, and your product surely isn't either.
My first job was to cold call on behalf of a charity for the blind, and I've also done a telesales job for short time, and got training in it.
First thing we learned the first day in both jobs was the way of structure a call to get interest. There were of course big differences, but a few very significant common takeaways. Incidentally there's a lot in common with this and being a good conversationalist or even generating attraction:
* You need to offer value. That means, you never ask to get anything off the bat. On the contrary, you seek to get them to feel that you're going to offer value.
* You set up drama that they want resolved. E.g. you offer insight about some situation that is emotional to the listener. For the charity for the blind, this was of course about creating sympathy. For the telesales, it was about describing some scenario that corresponded to a need the customer felt strongly about, such as spending more time helping their children read (the company sold children's books).
* You get the listener invested and hopefully make them contribute details to the scenario from their own background; e.g. explaining the problems with their business, for example, and starting to look for ways you can help them.
* You make statements that gets implicit buy-in from the listener unless they object. People don't like to object, and if this is done subtly, people will find themselves accepting your statements even when they initially disagreed with them.
* Then you give the customer hope that you can help them make things better. You've established yourself as having high value to them.
If you do it right they will ask you what they can do or how they can buy your product.
The overall structure is to start on a friendly high note, create drama and tension and bring the emotions down, then resolve the tension and offer up a solution while bringing the emotions up. Think Hollywood tear-jerker.
The scripts you quote on that page fails in that they don't set up a conflict or any tension that you can resolve for them. Just some bland statements about "cutting the nonsense".
I'd have done something more along the lines of "I'm sure that like lots of other [small,big, type-of business] businesses (implicit buy-in to your statement, putting them in a group they identify with), you've been hit with chargeback fees that were totally bogus [addressing a conflict] and have had to fight with your processor to recover funds and (more similar stuff)... (ask how it's impacted their business, and show them you sympathize). What do you think you can do about it? (listen to their feedback). Well, we have a report that helps you solve some of these problems. (wait for them to ask what it costs) We'll e-mail it you for free."
On top of this, voice, intonation and the level of excitement you manage to project makes a massive difference - the biggest problem in the training at both jobs was to go from sounding like you read from a script (because you did) to projecting well enough that you came across as believable. In my own experience, this latter is so much easier when you call yourself, rather than outsource it.
(EDIT: fixed formatting)