look at the site from chrome when logged into google create a link from another site to your site submit to google add it to google webmaster tools
More detail about your website could be useful. First add your website at : google.com/webmasters/tools/submit-url?pli=1 Now add your website to Google webmaster tool. Create a link from another site to your site as @sarahk said and ping the website where you have created your link in any ping tool. You can use Bulkping.com. Now manually crawl your website and its all pages on Google webmaster tool. Remember to update sitemap.xml in your website too. Google it if you don't know about it.
Do you have webmaster tool? Does your website have a sitemap? If yes then submit your sitemap url through webmaster tool and wait for like 24 hours.
You should try to get some links related to your topic pointing to your site. Well you could also try to ping it
You will have to first sign up for google webmaster tools through your gmail account and then when you login, you will get option to add your website. Here's the link to webmaster tools: google.com/webmasters/tools/