You need to look into the Unit of Work pattern. Your UoW keeps track of the changes, so when you get your order from your repository and modify it, you call UnitOfWork.SaveChanges() which should persist all the changes.
Using Entity Framework, your DbContext is basically the Unit of Work but I would create a simpler interface around it so you can abstract it away for easier usage in your higher layers.
Regarding EF, I would recommend mapping your domain entities directly using the code first approach. I would also turn off lazy loading and all the magic stuff so you have full control and less "surprises".
Unfortunately I'm not allowed to share our code but we have all this working pretty effectively with the new EF6 Alpha 3. I would recommend you taking a look at Microsoft Spain's nlayerapp for some implementation examples. I don't agree with many of their design decisions (also, see this review), but I think you can draw some inspiration from the Entity Framework parts. Take a look at their Unit of Work implementation and especially how they have abstracted it away for easier usage in the higher layers, and how they use it in their application services.
I will also recommend looking into creating a generic repository to avoid duplicating lots of logic in your aggregate specific repositories. MS Spain has one here, but you should also take a look at this thread.