Oh man that is a HUGE question with such a myriad of answers :)
If the structure of your site is good, ie good title, meta descript, h1/h2 then that will work well + the human elements in that mix to cause click through on title and description. After that the big one is getting links to your site with the right keywords. If you want to be more aggressive about it there are a ton of things you can try.
Can I ask the site's genre? Happy to brainstorm some link building ideas.
Are you part of the moz.com community?