How do you start a letter of complaint?

One, you want to be very clear about what you're dissatisfied with. And only state the facts, not the emotion. So, yes, you may be extremely upset and distraught, but whoever you're sending this letter of complaint to doesn't need that because it's going to overshadow the real issue. Address the letter to whomever the appropriate person is. You could say something like, "I dined at your restaurant yesterday. Typically, I have a wonderful experience. However, on this particular evening, I had trouble with my server Kate. She took a long time to bring us our food. She was very curt with us. She took a long time to bring the bill.”