If the buyer is not working with a real estate agent and does not have representation, the offer would come directly from the buyer. Represented buyers can also write their own offer letter and have their agent submit it for them.
Your letter should explain why you're interested in buying the house and include details regarding your mortgage financing and expected closing date. Often, the key to writing the best offer letter is finding a way to connect with the seller on a personal level.
A letter can be in violation of fair housing laws. Seller's agents who accept them are opening themselves and the sellers up to lawsuits. If you are prejudiced toward one type of buyer or another, fine - just don't let it get put into writing.
Here's how to write a great house offer letter: Start with the details. Show you're serious. Introduce yourself. Flatter the home seller. Keep the letter short. Go the extra mile. Examples of house offer letters.