There are two ways to do this (in fact many ways !) and theare are the ways I prefer most:
1) You can zip the entire website and then send it over to the client who can then unzip the files and all the folders structure will still be maintained.
2) You can host the site on your server as a test site and provide a link to your clients to view it from their desktops.
Does this work even if the client doesn't have Dreamweaver or any other HTML-reading program besides an Internet browser (such as Explorer, Safari, Firefox, etc.)?
YES as long as you tell them the home page name to open first like:
default.html; index.html etc etc.
They just need to open one page and all their links would work on their Internet Explorer or any other browsers.
Once a site created to comply with W3 standards, they don't need to have dreamweaver or any such editors. Site pages are simple text files!