You have to read the last sentence in the next paragraph to get your specific answer. I borrowed a good letter example from a site with a lot of business templates.
First of all, you have to say the addressee's name, career, and you have to say "Sama", and it should be delimited with line breaks and followed by two line breaks (Or maybe carriage returns. I don't know the difference, or which is more proper). Then, you use はじめまして。 You do a line break. Then you do business type '株式会社(かぶしきがいしゃ)' and business name (they come in different orders because the official company name may have かぶしきがいしゃ before, and it may have it after, and you really have to get it correct), section name (営業部の部の意味は"section") and のyour name, then と申します(もうす). 申します 'it's said this way' and has the same meaning as と言います, but it's 謙譲語(けんじょうご). It has the humble tone because it's humble language, and it says that you're speaking to someone who is in a higher place, kind of.
突然のメール､失礼いたします is the greeting. It means: "Sorry for the sudden message."
突然のメール､失礼いたします。 <<(THIS IS THE GREETING)
You can inspect the rest of the letter, yourself, below. This letter is a request for a guest speaker from a high-ranking person at another company, Nakamura-Sama (中村 裕子様). It's a standard 'request' letter, when you're not asking for any specific kind of favor; however, there are letters for some specific kinds of requests, and you should be careful. At the website I mentioned, there are templates for other things that you can ask for. For example, there is a letter requesting permission to relocate, from an employee to his boss, and there are many types of templates for to request that someone take action to correct a mistake of some kind. The kind of mistake they want corrected makes the letter's content change dramatically.
株式会社 山田商事 営業部
山田 太郎(ヤマダ タロウ)
TEL：066-9999-9999(直通) 066-9999-9999 (代表)
I am also afraid that I may have given you wrong information because business manners are so specific. If you are worried about a letter, you should post the specific letter in a question to make sure that you're writing it correctly. There are so many differences between two different letters with almost the exact same intention that each letter should warrant its own individual post.