To begin with, submit a sitemap to Google and Bing webmaster, this will help you getting started with SEO. Do the follwoing things and your website will start appearing on Google search results.
1- Keyword research and analysis (Use Google Keyword Tool)
2- Add those keywords to your meta tags and include description
3- Create a Google Analytics account to track your website conversion
4- Create a blog page for your website, WordPress is recommended since it's search engine friendly and easy to use and keep updating blogs on a regular basis
5- Become a guest blogger
There are many other methods but these are few simple things which will help your website get ranking on Google.