Start with the machine, not the paper. Find the data plate or the label on the unit, and copy the model number and the serial number exactly as they print. Keep the letters, any hyphens, and the spacing. Paper gets matched character by character.
Then open the paper and find the lines that name the equipment. Look for the model, the serial, the install address, and the installer's name. Mark each line that matches your note. Mark each line that does not.
Pay attention to quotes. A quote is often written before the unit is chosen, so it may name a model that was never installed. Ask for the invoice or completion record that names the unit that went into your house. The warranty paper you rely on should follow that record, not the quote.
Check who is named as the party to call. The paper should name the company or manufacturer that stands behind the terms. Write that name and its contact line in your folder. Then confirm how a claim is submitted and which steps, if any, are your job.
If a part has been replaced or the whole unit swapped, note what changed and when. Ask the paper whether it follows the original unit or the replacement. Do not assume the answer. Get it in writing.
What to keep. Photograph the data plate, the invoice, the signed page, and any registration confirmation. Put them in one folder, and keep a copy somewhere outside the house.
A match tells you the paper is talking about your machine. It does not tell you what the paper covers. For that, read the terms themselves, including the definitions and exclusions.
For planning, use the published service life figures on the appliances ranked by typical service life list, and count from your install record.