Since Chrome 56 came out in January, Chrome marks pages with a password or credit card field "Not secure" when they are served over plain http, and Google has said it will eventually do this for all http pages. No wonder so many sites are moving to https right now.
If yours is one of them, don't forget your sitemap. A checklist:
- Redirect every http address to the same https address, with a permanent (301) redirect.
- Make a new sitemap with the https addresses: add your site with its https:// address in your control panel and run it. A sitemap with the old http addresses sends search engines through all those redirects.
- In Google Search Console, add the https version of your site as a new property and submit the new sitemap there. Do the same in Bing Webmaster Tools.
- Update the Sitemap line in your robots.txt, if you have one.
- Check your own links, images and scripts: anything still loaded over http gives a warning in the browser.
Expect some ups and downs in your search traffic for a few weeks while search engines move their index over. That is normal.