Use a basic four sentence structure:

1 State the argument that you're responding to
Is it a particular article?
What prompted you to write this?

2 State your position.

3 Provide Evidence.

4 Provide a Solution - say what should be done.

It’s good to infuse wit and personality into your letter, but it’s not a requirement: most of the letters to the editor in our national press are fairly dry.
It’s also good to start off with a slightly more emotion-based appeal, and continue with a fact-based solution

Example of a letter using this structure:
Why is it that the world recognises our magic Basin Reserve roundabout but the New Zealand Transport Agency doesn't? (Basin to join list of 'magic roundabouts', April 10)
Surely a cold, grey, shadow-casting concrete flyover will remove the magic from the roundabout and the Basin Reserve.
Maybe NZTA could consider another option to just extend Kent and Cambridge Tces to Adelaide Rd under the Basin using a ''cut and cover'' tunnel for Newtown to the city traffic and leave the roundabout as is for all other traffic?

Tips
The paper won't publish letters that are too similar, but they might publish several on the same topic if they come from very different angles.

For example: With a particular transport project you could write from the angle of being a young person, or your experience of driving, or not driving, or as a student of economics, or from the broader context of climate change...

It's good to draw on personal stories connected to the topic.