if it the functions file, the child theme is loaded in conjunction with it's parent, the child being loaded first.
If its the index.php file, you need to make sure your WordPress version greater than or equal to 3.0. Otherwise, your index.php file won't overwrite.
A lot of reworking of themes has happened, so make sure you check out the documentation on themes and more specifically child theme overrides.
Basically, to overwrite another file, simply make sure it has the same name. If your trying to overwrite a theme specific (ie. not WordPress default theme file) file, it won't work. You'll have to overwrite at he WordPress specific theme name and go from there.
For example, if you are trying to override
page.php, just place a
page.php file in your child theme directory.
page.php includes or requires some specific file in some parent theme sub-directory, you'll have to override
page.php and change the include location.