You will need a cover letter whenever you send a resume or application form to a potential employer.
The letter should capture the employer's attention, show why you are writing, indicate why your employment will benefit the company, and ask for an interview. The kind of specific information that must be included in a letter means that each must be written individually. Each letter must also be typed perfectly, which may present a problem. Word processing equipment helps. Frequently only the address, first paragraph, and specifics concerning an interview will vary. These items are easily changed on word processing equipment and memory typewriters. If you do not have access to such equipment, you might be able to rent it. Or you might be able to have your letters typed by a resume or employment services company listed in the yellow pages. Be sure you know the full cost of such a service before agreeing to use one.
Let's go through a cover letter point by point.
Each letter should be addressed by name to the person you want to talk with. That person is the one who can hire you. This is almost certainly not someone in the personnel department, and it is probably not a department head either. It is most likely to be the person who will actually supervise you once you start work. Call the company to make sure you have the right name. And spell it correctly.
The opening should appeal to the reader. Cover letters are sales letters. Sales are made after you capture a person's attention. You capture the reader's attention most easily by talking about the company rather than yourself. Mention projects under development, recent awards, or favorable comments recently published about the company. You can find such information in the business press, including the business section of local newspapers and the many magazines that are devoted to particular industries. If you are answering an ad, you may mention it. If someone suggested that you write, use their name (with permission, of course).
The body of the letter gives a brief description of your qualifications and refers to the resume, where your sales campaign can continue.
You cannot have what you do not ask for. At the end of the letter, request an interview. Suggest a time and state that you will confirm the appointment. Use a standard complimentary close, such as "Sincerely yours," leave three or four lines for your signature, and type your name. I would type my phone number under my name; this recommendation is not usually made, although phone numbers are found on most letterheads. The alternative is to place the phone number in the body of the letter, but it will be more difficult to find there should the reader wish to call you.