I want to add a text-entry field to each instance of a product added to the shopping cart

I put this out earlier as a "Is there a module that can do this" question, and it turns out there is no such module. Where would I start looking to find the hooks to add this module in? I know approximately where I want it in the purchase workflow: just after the "add to cart" button has been presses, I want a page to display that says,
"Type your custom imprint here." then have a continue button that takes you on to the cart display. I would also like the data of the custom imprint field to appear on the shopping cart page with an edit button to take the user back to the edit page to fix spelling errors. Finally the field info, properly linked to the user, order and SKU has to go to the notification email so the supplier gets the imprint right.

I have never done one of these before, and any help will be considered fantastic.

-Wolf