Yes.
1. Create the custom error page. If it is for 404 errors, I name it 404.html
2. I put them in their own directory, called error or errors.
3. Open .htaccess file and add line(s):
ErrorDocument 404 /error/404.html
ErrorDocument 403 /error/403.html
ErrorDocument 500 /error/500.html
for the ones you have created. You can also do it with .php files if you want to get fancy in what the error page displays.
If you are talking about WordPress or Joomla or other CMS scripts, they have their own ways of creating custom error pages (usually using the theme you are using so they fit in).