If you are seeing links in the search engine results pages that go to an old site of yours, this is because the old site is currently in the search engine's index and the new site has not yet been indexed.
When you switch your domain over to a new site, that does not remove the old site from the search engine's index. What will happen over the next few weeks to few months is that the search engine will return to your domain and see that the content has changed. When it picks up the changes, it will replace the old site with the new one. This will be done gradually and you can expect the indexing to take anywhere from a few weeks to a few months.
What you should do is verify your site with Google Webmaster and submit a Sitemap, this will help. Here is a link to the tutorial: Google Webmaster Tutorial.