Hi,
You can look at your Google Webmaster Tools account to know what are the search queries that your visitors used to land on your website from Google. You can also look at your web analytics data (like Google Analytics, SiteCatalyst etc) to know this data but as Google started encrypting the search, you won't be able to see the complete picture of your keyword data that is drving traffic from Google. If you don't have an access to webmaster tools account or web analytics, you can try using tools like SEMrush to have a fair idea about the keywords that are driving organic traffic to a website.
Coming to the strategies, useful, relevant, updated content stands at the top followed by backlinks coming from other topical niche sites, good blogs and forums, authority websites like .gov, .edu, .org so on and so forth. If you can come up with top notch content, half the battle is won as good content is a natural link magnet. Those were my two cents my friend. Good Luck and please post back in case you have any other queries in this regard.
Best regards,
Devanur Rafi