Google search is still showing the old website in the search results

Selected answers from the Dumb SEO Questions Facebook & G+ community.

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  Lyndon NA: You have setup 301 redirects from old URLs to new URLs?When I land on a page from your old site, I should automatically be transfered to the same/related/similar page on the new site.1) It`s a better experience for users2) You don`t lose traffic from old links/bookmarks etc.3) You keep the majoritry of the rankings for the old pages, and they are given to the new pages.Otherwise, you are simply building a new site and starting from scratch.IF you have redirects in place, and they are detected - then you have to wait for (a) G to crawl the old site and see the redirects(b) for G to process the redirects (c) G to crawl the new URLs and (d) G to associate the date from the old to the new. This can take a few weeks (depending on how popular/import it thinks your old site is.In GWMT there was a tool for domain transfers - I assume that it`s there in Search Console - so you might want to make sure both sites are setup in Search Console, and then tell G that Old is moved to New.
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  Tamás Somogyi: Plus also check the backlinks. Make sure that all URLs which become backlinks are also redirected to a valid RC:200 page.
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  Neeraj Pandey: +Meenu Makan why you are having 2 websites live at the same time when they are duplicate ? there are the site move guidelines which could help you at this time or after some time. Google will consider them as 2 separate websites if you don`t hint it and it might impact the organic traffic & ranking