Before you apply

Have you got an up-to-date and relevant CV? Even if you can't send it as part of your application, the process of writing it will help you focus on your strengths and attributes

The application form

If the employer states that CVs will not be considered - DON'T send one. It will not be looked at, and will get up the selector's nose!
Read the job and person specs carefully, and address each point in turn - demonstrating how your qualities/experience/knowledge/interests fit the specification. Selectors will invite for interview the people who tick the most boxes.
If you are completing the application form on a computer, you can copy and paste the job and person specs into the appropriate boxes in the form and write your responses below the headings. This way, you know you've covered all the points.
If you don't seem to fit a particular point directly, think about equivalent knowledge or experience in a different sphere, and explain how this is transferable to the job you are applying for.

The covering letter

Applying for an advertised job (with application form or tailored cv)
The covering letter is the first thing that the prospective employer sees, and in job hunting first impressions are vitally important.
It does not need to be long – the employer will be looking for a concise and clear presentation from you. You only need three or four paragraphs.
The first paragraph sets out what job you are applying for, and how you heard about the vacancy.
The meat in the sandwich is your ‘sales pitch’, providing evidence and information about you to support your application, and telling the employer (briefly) why they should consider you above other applicants. You could hit the employer with three bullet-pointed reasons why they should employ you.
Finally, include a paragraph thanking the employer for reading the letter and expressing your hope that you will be able to discuss your application with them at an interview.
Make sure that the letter is laid out well, and that grammar and spelling are correct. Get someone to check the letter before you send it – you won’t get a second chance.
Check that you have addressed the letter correctly - read the advert carefully. Mis-spell the employer’s name, and your letter may not even get opened.

The speculative letter (with tailored cv)
If you are writing to a company ‘on spec’, rather than in response to a particular advertisement, you need to take a different approach.
You need to do a lot of research on the company, and clarify in your own mind how you might fit in.
Address your letter to the HR Director, or to the head of the department you hope to work in. If you know the name of the person, address the letter accordingly.
In the first paragraph, introduce yourself briefly. And explain why you are approaching this company.
In the second paragraph, demonstrate that you have a good understanding of the company, and explain why you think they should employ you. Highlight some hard skills that are relevant
Follow that with a paragraph painting a picture of yourself - your personality and soft skills.
Finally, thank them for reading the letter and cv, and express the hope that you will be able to meet them to discuss your suitability.