I redesigned and reprogrammed my site. Some of the content on my new site is same as my old one When I give google search on the new site. I am getting result from my old site- the links are from there. what should i do , so that i get the correct results.
The old content will stay up until it is re-indexed by Google, currently it is probably just cached. To tell Google about the new site, consider opening a Google Webmaster Tools Account which will allow you to control (to some degree) what is indexed. It allows a direct upload of a sitemap which should help. Without knowing specifics, tough to give a more direct answer
Google webmaster tools is a good idea since you can set how often google bot crawls your site. Really though you will need to wait for a google deep crawl to have your site reset in the serps.
If you have same content on the new site, then it is best if you have a 301 redirect so that you are not bit by a duplicate penalty. As for the old links on google search, it will take some time for google to display links to your new site but it should be soon
You have to wait until google recrawl your site and index the newly amended website. In most cases, blog usually getting faster update due to it's ping availability.