The hardest thing about that transition is that many of the examples you will see have most if not all of the code in the aspx.cs code-behind page.
If you have been following good design and coding methods in the WinForms world you know that the more you can separate the presentation from the classes and objects you design the easier your design is to test. It's the same in the web world.
It will take a bit to get used to the page and control lifecycle, and a few objects are more different than you might first think - but it should be a fairly smooth transition.