Not sure how detailed you need be to be.
Basically on the product archive page you query the products. Although if you created a custom post type for products and create the template file named archive-products.php then this is done for you.
Then you loop through the products just like you’d normally do and for each product you’d do the same thing you do on the single product page, getting the fields from the related manufacturer.
A can’t really be more specific than that because I don’t know how you’re storing the products and manufacturers or what type of field you’re using to relate them.
