These fours steps:
1. Optimize the website for page speed. The faster it loads the higher it will ranks:
a. Use Website Speed and Performance Optimization to identify what to fix.
b. If you are using a CMS, use as few plugins and modules. Especially, if they are 3rd party.
2. Do on-page optimization of title, H1, H2 etc - Use mozbar as checklist.
3. Write shareable/viral headlines. Study Buzzfeed - they know this stuff. The more shareable it is, the more possible backlinks.
4. Make sure you add elements that keep users on your site once they have landed. This can be related content, freebies etc. Drive down bounce rate. The lower the bounce rate, the higher the likelyhood of ranking.