Refer to the manage_posts_columns filter, and also the manage_posts_custom_column action.
Here is a really old tutorial, linked from the Codex, that might be instructive. (Caveat: it’s from 2007; some things might be out of date.)
Edit
The above hooks are for the manage posts screen. To remove/add meta boxes to the edit post screen, see add_meta_box() and remove_meta_box(), which can be invoked inside a callback function hooked into add_meta_boxes.
Here’s a tutorial for customizing meta boxes on the edit-post screen.