Great copywriting is both art and science. On a website landing page, it’s absolutely key to success. One of the ways I like to think about designing such a page is to consider the page to be visiting the prospect, not the other way around. That way, you begin to think about the defences which the prospect puts up, and how to talk your way around them.
The first thing to do is to grab the prospect’s attention. They might have clicked on the link to your page, but they’re already thinking of leaving (we all do this, instinctively). Be interesting, both in your design and your headline statement.
Then, having stopped them from clicking the back button, be persuasive. Relate to your audience by showing you understand their needs and can help them. Remember, they know you’re a business, not a charity, so don’t pretend otherwise. You want to get into a transactional relationship with them, where both parties can benefit. So be grown up about it.
And if you’re waiting for more, there isn’t any. You’ll find entire books on the subject of great copywriting to maximise conversions, but they’ll all distill down to something like the two steps above. If you don’t study the subject any further, at least bear those in mind.