ASPX files usually will have the UI and will which is usually HTML tags, some ASP.NET server control embed code (which ultimately produce some HTML markups). ASPX.CS file (usually called "code-behind") will have server-side coding in C#.
If needed, I would relate ASPX page to View and ASPX.CS to Controller action methods.
You have to remember that in webforms, there are ASP.NET controls we will be using in the ASPX file to render some HTML. Examples are TextBox, DataGrid, etc. In MVC, there is nothing called Server control. The View will be pure, handwritten HTML.
If needed, you can create a Hybrid project which is a combination of MVC and webforms. Scott has a post explaining about it here.
No ViewState in MVC :)
When switching from ASP.NET Webforms to MVC, One important thing you have to understand is that MVC architecture tries to stick with the truth that HTTP is stateless. There is no viewstate available in MVC. So you need to make sure that you are repopulating the data in every HTTP Request, as needed. Folks usually run into problems in loading DropDownlist in MVC. There are a lot of answers here in SO about how to handle dropdown lists on postback (when form is posted).
I suggest that you look into some beginner-level tutorials on ASP.NET MVC and start building your app step-by-step, and if you run into any issues, post a (new) question with relevant details.
Good luck, and welcome to the wonderful world of MVC. :)