add a product in the archive programmatically

I want to create a button that:
open a .net page
add a new product in the archive
add the product in the shopping cart
Which is the simple and the better way to do that?
Where, in the documentation, can I find useful information for what I need?
Thanks

Would you clarify "archive"?
Are you trying to create a new Product / Product Variant?  (Where would you get the new info from? )