A few people asked me to expand on my format for a covering letter to an agent, so here it is, all to be fitted on one page.
1. Why you're writing to them. You've heard them speak or read an article they've written. Maybe they represent an author who you admire and hope to emulate. It should be specific which shows that you've bothered to do some research which in turn shows a professional outlook.
2. Brief summary of your book. Length, genre etc. Then a few sentences about the theme of the book. This equates to the scriptwriter's elevator pitch, where you imagine you're in a lift with someone who could buy your script, but you've only got a minute to sell it to them. Be clear about what it is you're selling.
3. Market position of the book. Essentially, who's going to buy it. This could be phrased as 'It will appeal to readers of...' and then name a couple of authors, rather then a demographic. Depending on the book, you might want to combine paras 2 and 3.
4. About yourself. Include anything that endorses you as a writer, such as articles published or short story competitions won. Also include any personal information that is directly relevant to the book, such as the book is about shenanigans in a school, and you're a teacher. Don't include anything else such as your friends think it's a wonderful book, or how very difficult it was to write.
5. Thank you for your time etc. I call this the 'I am not a loony' paragraph, so no demands that they get back to you within 48 hours, or copyright threats. Instead, pitch yourself as the ideal author, hardworking, full of ideas and enthusiasm, but also very open to feedback and direction. And don't forget the SAE.
The whole should be written in simple, straightforward language - you are after all hoping to have a long term business relationship with this person. Ask some friends to read it because, in your anxiety to get it right, it's very easy to come across negatively, and while they're reading get them to check the spelling and the grammar. And by the time you've done all that, you're probably feeling like giving up on the whole business and taking up watercolours instead. But persevere. Get it right just once, and you'll never have to go through this again.