How do I add to cart and send straight to Checkout?

From other sites and pages I want to Add to Cart and go straight to Check Out.

I am a .Net developer so I was going to pass order information into a new ASPX page that would be part of NOP install.

How would I do this and is there anything wrong with doing this?

You should have a look at the code of related controllers such as ShoppingCartController and CatalogController. You can use the services to do the trick for you. :)

I'm a WebForms developer so there's a huge learning curve for MVC.

How would I call a method of the controller from an .ASPX.CS page?

Hmmm... Did you mean you are placing a WebForms page inside nopCommerce? Or your WebForms project is a separate project from nopCommerce. :P

I could do it either way. I would prefer to do it as an aspx page that is part of the nop web application.

In fact it's Okay if you are not familiar with MVC, because what I am suggesting is not to invoke MVC from WebForms. What I suggested was for you to look at the related controllers, and see how those controllers makes use of the various services. If you want, you can directly view those services under "~/Libraries/Nop.Services". But since there are so many services, it'll be overwhelming for you to know which service does what. So I suggested you to look at, for example, ShoppingCartController and examine the services used; it's easier like this. :)