What is a 404 page? It is a page that tells your visitors when they go to a specific page that it no longer exists.
Using a custom page for this is a benefit, especially to search engines like Google. The search engines index websites and all of their pages, including the 404 page.
One way is to redirect, but this is not highly encourageable. You could make a redirect, but the search engine (ex. Google) would index the page and your site when searched could read “Page not found” instead of your homepage. In doing this procedure, you could accidentally have the search engine alter the indexing by removing non-existent pages. So, in other words, that same re-direct could get your homepage de-indexed by accident.
The other way, is the custom page. You can do this through your content management (ex. CMS software like WordPress) or your regular html pages. Instead of just posting “404, page not found” or “you have reached this page out of error”, here are some suggestions:
1. Make your page informative. You can add “Sorry, this page does not exist”, but do not stop there. Add a way to contact you whether it be an email address posted or a contact form.
2. Add a few special links to the page that might interest your visitors. Four or five links might be nice.
3. Conform your page to match your site. A plain 404 is an annoyance to deal with already and having little information will make the visitor give up and go elsewhere.
4. Make sure to add your sidebar/ navigation to the page. It is as usefull as the special interest links and widens the possibilities that your visitor will stay and surf your site.
5. Verify that your 404 page actually returns a 404 error. You can do this by using Google Webmaster Tools.