Custom 404 Page Not Found Error page for SharePoint 2013 Site Collection

SharePoint 2013 is shipped with a default "Page not found" Error page in "Pages" library in publishing Sites (http://intranet.crescent.com/Pages/PageNotFoundError.aspx) which works automatically when a user hits a non-existent URLs.

We can either customize this page or create our own page and set as a page not found error page. Here are the steps to create a custom 404 page not found error page:

• Go to Site Contents, Pages Library and Create New Error Page
  
• Customize the error page with your own styles and images
  
• Use PowerShell script to set the new page as default page not found error page.
  

  $site = Get-SPSite "http://your-sharepoint-site-coll-url"
  $site.filenotfoundurl = "/Pages/PageNotFound.aspx" #Relative path

Using SharePoint Designer to set Custom Page not found error page:
You can also use SharePoint designer to set the custom page not found error page: Here is how:

• Open your SharePoint 2013 Site in SharePoint Designer 2013
• Select the Site object in the left side treeview, Click on Site Options button in the ribbon 
• Assign the "vti_filenotfoundpage" property of the site to a Custom Error Page that you created.
  
• Don't forget to hit Save button to commit your changes.

The above is applicable for setting  custom error page at site collection level. If you want to apply it at web application level, refer my another article: Custom 404 Page Not Found Error Page for SharePoint