Your letter should start with "Salutations", showing the closeness with your friend.
Remember not to write full name of your friend, it is preferred to use only first name, 
e.g if you are writing the letter to your friend Daniel Radcliffe, you are advised to use only the first name of your friend: 
Dear Friend,    ;   Dear Daniel,

Then you must begin directly with the introductory paragraph having the vital contents:

• Comment about the news from his letter

• Apology, along with reason

• Purpose of letter   
  A good example for you written by me ;p
       "Dear Friend
  It was good to hear from you. I know it was wrong of me for not writing something to you sooner, but I've been busy carrying out an event organized by me. How were your holidays? Anyways, I was eager to drop you a line about this event and you won't believe what I did!"        

Now, analyzing the paragraph content wise and as well as language wise.

-> It starts from Salutations, "Dear Friend" , then going towards the paragraph => "It was good to hear from you" This shows that you and your friend are in touch with each other and this also shows kind of personalization between you two. Moving forward, "I know it was wrong of me ..." this is an important part, the apology you are giving to your friend along with the good reason "but I've been busy with ..." is what the reader would want to read. Then comes the purpose of letter which will act as a back bone for the reason given in apology.
Remember not to write too long introductory sentence and as said before use good and precise vocabulary, which I sooner am planning to upload here on my website.
And the more interesting and descriptive your letter is, the more grades are what will be written in your account :) 

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