Share your unique angle
Letters and op-eds are much more likely to be published if they provide a unique perspective on the topic at hand. And it's important to speak from your own perspective - authenticity should come through. Don't be afraid to be controversial. Editorials that sound generic or common are unlikely to be published.
Respond quickly, and be brief
Letters should be ideally submitted the same day the article they respond to is published; no later than the following day. There are some exceptions to the 1-day rule. Responses to articles in publications with longer cycles - like a weekend magazine or the Sunday Times - have a longer shelf life.
The more concise, the better. Be sure to edit down your letter after you draft it; ideally you want to make one point, and no more. Each publication has its own word limit, typically no more than 150-250 works; for letters and 650-700 words for op-eds. That is why it is important to make every single word count.
Finally, if you don't get published the first time, try, try again. Practice really does make perfect when it comes to honing your writing skills.