There is no magical formula that will push your website higher up in the SERP's (Search
Engine Result's Page) but there are plenty of techniques you could apply that will allow your site to rank higher than it probably is at the moment. Google and other leading search engines use a complex algorithm to determine which websites should rank higher than others, this algorithm can incorporate over 200 criteria that analyses every individual aspect of a website.
There are 2 main areas when it comes to improving your ranking in the SERP's which are: Keywords and Backlinks. These are the areas where you will want to improve and build a strategy for.
If your website lacks the correct keywords that relate directly to the contents of your site and industry then there will be little chance that search engine spiders (that crawl websites to determine which sites are more relevant than others) will place your website high in the results page. To give your site the best chance of ranking on the first few results pages it is imperative that your Meta tags, Meta descriptions and headings all contain rich keywords that can easily be crawled by search engine spiders.
On-page factors are only half the story when it comes to SEO and optimising your website well enough for search engines. The second part of SEO concerns your link landscape: how many inbound links your site has and the quality of those links pointing back to your website.
If you want to rank high in the SERP's then it is important that your site gains enough backlinks so that search engines can identify your site as being of high importance in your specific field/industry. In order to acquire backlinks there are multiple methods such as article syndication (writing fresh content and distributing it on article websites), reciprocal links (link exchanging with other similar websites), buying links (not recommended as Google may penalise for this type of link acquisition) and other methods such as having a link pointing back to your site in your signature at the end of a blog post or forum post.
It is important to mention that when it comes to backlinks it is the quality of the links and not the quantity that is important. Having backlinks to your site that come from a link farm will not offer you much value if any and may even hinder your site as Google or other search engines can see that you and linked back to a disreputable website.