You do not change Google results. Google changes Google results.
This happens when Google crawls your site and updates its index. Depending on its priority, this can take from less than an hour to several weeks. At the beginning, before Google realizes how important your site is and how often it changes it will take longer. Just be patient.
Any new link to the website can help it along but the placement of that link is critical. If an article is posted in a news service about your new site for example, it will be found much faster is someone just comments on a random blog. If you have changed the site structure as opposed to the page layout, submitting a new sitemap through Google Webmaster Tools can help.