You have this win32 API

BOOL DeleteFile(
LPCTSTR lpFileName // pointer to name of file to delete
);

You have a method for selecting a file:

BOOL GetOpenFileName(
LPOPENFILENAME lpofn // address of struct with initialization data
);

This creates a Open file dialog that returns the name of
selected file. You can customize the properties of dialog
box with the structure OPENFILENAME, i.e.: a dialog box
with a title "SELECT FILE TO DELETE" and a filter *.* for
all the files.