Typically, you do the primary development of your HTML5 and CSS3 website on a server that isn't in public view. Follow these simple steps to take the site to production:
Test your design.
Do some usability testing with real users. Watch people solve typical problems on the site and see what problems they encounter.
Proofread everything.
Almost nothing demolishes credibility as quickly as sloppy writing. Get a quality proofreader or copy editor to look over everything on the site to check for typos and spelling errors. If your page contains a specific type of content (technical information or company policy, for example), have an expert familiar with the subject check the site for factual or content errors.
Prepare the online hosting environment.
Be sure that you have the server space to handle your requirements. Make a copy of your database and test it. Check the domain name to be sure that you have no legal encumbrances.
Move your site online.
Move the files from your development server to the main server.
Test everything again.
Try a beta test, where your page is available to only a few people. Get input and feedback from these testers and incorporate the best suggestions.
Ensure you have a maintenance agreement.
Websites are complicated, and they will have a long lifespan. Make sure you have an agreement in place that clearly indicates your ongoing relationship with the project. You should generally have the client sign off that the project is complete and build in some kind of contract for on-going support.
Take a vacation. You earned it!