As Yorkshire man said it is a combination of things. The first thing to do is make your code search engine friendly. I notice your "meta description" tag is on the long side at over 350 characters, Google cuts off the descriptions at about 150 characters. Also I noticed there is no "meta keywords tag" which some people argue is useless but it works for me. You also only have an "h1" tag and no "h2" and "h3" tags giving the page very little structure to the Google spiders which will crawl your site. If all of that has gone over your head speak to your web designer as they are all easy fixes.
After that its all about back links nowadays, that is links back to your website from other websites just like you did in the initial question. Relevant backlinks are the best but face book, google plus, yell, gumtree (at a cost) and others can provide quality backlinks. Hope this gives you a starting point.
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