Applying for an unadvertised job is an attempt to create an opportunity for yourself. Because the company isn't actively seeking new, talented people, your cover letter has to grab the hiring manager's attention and be memorable. If there isn't a job opportunity available at this company now, there will be in the future, and a memorable cover letter expressing interest could help you secure that job later on.
Call the company that you wish to approach and find out the exact person to address, plus his title. Sometimes this information can be found on the company website. Try your hardest to find a specific name rather than just opening the letter with "Dear Sir or Madame" and sending it to the human resources department.
Start with the standard cover letter format. Put your address in the top left corner, with your name on one line, your street address on the next line, your city and state and zip code on the last line. Skip a line and write the complete date. Skip a line and write down the full name of the person you are writing to. Below that, write her title. Below that line write the company's street address and directly underneath that write the city, state, and postcode. Skip a line and write: "Dear" plus the full name of the person to whom you are writing.
Skip a line and start your first paragraph. State your name and explain that you are writing to inquire about possible job opportunities with the company. Explain how you know about the company and why you want to work there. Feel free to be complimentary and knowledgeable about the company, after all, this is a team you want to join.
Skip a line and start your next paragraph. Explain your skills and background. In an enthusiastic manner, explain why you think you'd be a good addition to the team. Be specific: this is your chance to talk about detailed points or experiences from your resume that you think are relevant and, more importantly, that you think will impress this employer. It's a good idea to have your resume in front of you so you can reference it as you write.
End your letter by directly and politely requesting a job interview and indicate that you are happy to meet at his convenience. If you're simply writing this letter to acquire more information about possible opportunities, state that fact and consider including a self-addressed stamped envelope with your letter, or your e-mail address.
Skip a line under your last paragraph and write: "Sincerely Yours," skip three lines and type your name directly underneath that closing phrase. Print out your cover letter and sign it just above your typed name.