Writing a letter of advice is, in many ways, no different from writing an essay. An introduction should state the purpose of the letter and provide a brief outline of the advice to be offered. Since advice is not necessarily welcome, an introduction to a letter of advice should probably be as diplomatic and persuasive as possible. For example, if I were writing to a friend whose drinking seems to me to be a bit out of control, I might begin like this:
Because you are such a dear friend, I always care about your mental and physical health. I have noticed that when we go out for dinner, you have at least three glasses of wine, and this concerns me for a few reasons. First, I worry about your driving. Second, I worry because I know you are trying to lose weight and these are empty calories, and third, I am concerned about the long-term consequences for your body and your mind.
I am not sure whether you are talking about writing a letter of personal advice, educational advice, or business advice, but the principles remain the same, no matter what the subject of the advice is. One way to get a sense of this might be to look at some published letters of advice, for example, the one described in the link I have provided.