How do I type a letter on my headed notepaper sent to me as an attachment?

iPad doesn't provide support for stationery within the mail app.

Usual approach here is to use a word-processing tool (Apple iWork Pages, for instance) and inserting an image containing the header into the Pages document. Using an image as a background also works, but is less common.

Put differently, Pages or similar can do what you want—getting a digital version of the header would be preferable—but a tool such as Mail just doesn't have the control required for what you're seeking, both on the sending end of the message and particularly not on the receiving end of the mail message. Mail client rendering is all over the place.

A PDF generated from some text and graphics and images created using Pages or another tool, yes, that can have a fixed format that's determined by you, and that PDF can be attached and mailed.

Apple iWork Pages is free, and is available on Mac, iPhone, and iPad.

Here's an introduction to Apple iWork Pages on iPad:

Pages User Guide for iPad - Apple Support

To confirm my understanding of the question, you wish to use stationery ("headed notepaper"?) as a background image when sending mail messages from within the iPad mail application?

Or are you looking to add typed text onto some document you've received as an attachment? If so, what sort of document?