A good way to learn how to work with ASP.NET is to take a web template and start making it into a functional website.
For example, if you download this template you can see that it's a pretty straight forward business style site. Home, Projects, Services, Downloads, About and Contact are the main sections. The template also has a some additional buttons and links. These are all pretty good places to start learning how to create a site.
First thing, create a masterpage from this template. This is where you'll learn how to tear apart someones HTML and where to start placing content Templates and to start thinking about what can be a user control or reused (main menus, footers, sidebars controls etc.)
Next steps would be do go ahead and flesh out the folder structure of the site and dive in making the those default pages for each section. A learner will quickly see how a site is created from a master page and learn the little quirks of images and stylesheets and how to get around those as you dive through folder structures.
Now it's your choice. Pick a section and start having them dive into it. Products would give you a way to use a database, querystrings, forms, etc. How to pull data, how to display it and how to save it. Downloads would be a place where you could learn how to manage content for a user. What little admin tools a site would need to manage it. Services and About can be CMS driven pages. Once again data driven, but still different from the Products section. The contact forms would give them the option of leaning about using Email from inside of a .net application.
Now once you get your learner working on this, they might actually end up with a pretty usable site/product that they could actually sell or reuse in a 'for real' project. Take your time teaching them, go slow on each section and I'm sure you'll get some good input back from your learner.
Hope this helps you.