How to add custom input fields to a new Custom Post Type?

I just created a new custom post type, Shows. It’s for a music site, so that post type is all about upcoming concerts.

I’d like to customize the input fields for this post type. By default, the fields include things like title, then text editor box, trackbacks, custom fields, etc.

How can I get rid of these and only include my own specified boxes? I found this site https://bit.ly/a55Hc2 and now know how to include simple input fields where a user types in something, but how could I include something like a box where a user uploads a single image, or a field where the little calendar pops out and the user can select a date (this, for example, would be the upcoming concert date).

There are many sites out there on how to create a custom post type. I’ve got that down, but now the input boxes are hanging me up.

I’m using Custom Post Types UI plugin to make that part of it easy, but I wouldn’t mind seeing some more examples of customized meta boxes.