From my experience, successful letters to the reviewer have been very objective--guiding the reader to a specific line number in your original manuscript and/or reviewed manuscript.
Often times the reviewer will say something like "the author failed to show that x is correlated with y," to which I usually write: "the authors wish to thank the reviewer for raising this issue. We have added a new sentence to clarify how x and y correlate (please refer to line 100 of the reviewed manuscript)."
Sometimes, the reviewer simply does not understand a passage of your manuscript. For example "the authors did not explain why the sky is blue," to which I commonly reply "the authors wish to thank the reviewer for raising this issue. We wish to bring the attention to line 200 of the manuscript where we say that 'the sky is blue because of xyz, as supported by Figure 1.' "
Sometimes the reviewer is just mean. Once, a reviewer wrote the following to me: "the author is encouraged to understand the basics of physics," to which I simply replied: "5 new references have been added on line 300 to support our claim that heavier bodies accelerate slower when acting upon an unchanged force, a direct result from [Newton, 1687]."
You can't be rude, but you must be succinct and show exactly where in the manuscript you address the issue raised by the reviewer.
You can then take 3 actions:
1. add a sentence to clarify the issue,
2. point to the reviewer that you have in fact explained the issue in the manuscript, or
3. add references that support your claim and weaken the reviewer's concern.
Some times, if your response letter is objective and clearly addresses all the reviewer's concerns, the Editor will accept your manuscript upon reading your letter and not send back to the reviewer for another round of reviews (this has happened to me at least 2 times before).