Edelweiss does not sell or distribute books, but simply acts as the platform on which publishers post their catalogs. You can discover upcoming titles, and create orders for them, but you’ll need to order those titles either from the publisher (usually via their sales reps) or through your preferred wholesalers.
If you do work with publisher sales reps, you can share your Edelweiss orders with them. They can then grab them in their Edelweiss account and submit them in that publisher’s preferred method. More about sharing orders with sales reps here.
Alternately, you can create an order in Edelweiss, export it, and then submit the order to whomever you like using your usual methods. It’s really up to however you prefer to do business. You can find instructions for creating your own custom order form here and more about exporting orders for Ingram, Brodart or Baker &Taylor here.