Before you start: take inventory
List every page on the current site with its address, title and whether it gets visits or calls. Search Console and your analytics show which pages matter. Export the list and keep it.
Keep what works
Pages that already bring in customers should keep their content, their main headings and ideally their address. Improve them in place instead of replacing them with something new.
Redirect every address that changes
If a page moves, set a permanent (301) redirect from the old address to the closest new page. Do not send everything to the home page. Test a sample of old addresses after launch.
Do not block the new site
Staging sites are often set to ask search engines not to index them. Make sure that setting is removed at launch, and that robots.txt does not block the live site.
After launch
Submit the new sitemap in Search Console, check the Pages report for errors, and watch impressions and clicks for a few weeks. Small movement is normal while Google reprocesses the site. A sudden fall in a key page means a redirect or indexing problem to fix.
Common questions
Will my rankings drop after a redesign?
They can move for a while, but a careful relaunch with redirects keeps the risk low.
Should I change my domain at the same time?
Avoid it if you can. Changing the domain and the design together makes problems harder to trace.
This guide is general information. Search engines change how they work and their guidelines; check Google's current documentation for your situation. Nobody can guarantee a ranking.