Search engines (eg Google/Bing) are essential to your website success. Try to cheat them and you'll be blacklisted. The thing to remember is that everyone is trying to be #1 for generic key phrases. There are two elements to success - what you control on your website (content & structure: "on-page") and what you do elswhere to promote it (pay per click advertising, links from other sites etc: "off-page")
Firstly let's look at the main "on-page" factors.
Ensure you have a different page title for every page in your website. Page title is the most important factor that influences your search engine ranking, after the domain name. Keep it under 80 characters.
This is the snippet of wording that search engines show in results. In conjunction with the page title it influences the ranking. However if your page content doesn't relate to the description and page title then it's irrelevant so make sure the combination of page title, page description and the actual content are all related.
There are a number of other invisible tags that your website should be using. These help search engines decipher things like your preferred logo/image, your business category and even what events you have coming up. If you use these tags then you can expect greater results from search engine listings. Ask your web developer about schema markup.
Imagine you're taking on a new head chef. You get 100 applicants, all at face value look capable of doing the job. But that's not point, you need to establish their authenticity and their trustability. Through interviewing and research and references you can ascertain which ones are more likely to be your preferred options.
This is how a search engine works. It needs to work out your reputation and trust level. It will look at the quality of your content, how many people are searching for you, how long they hang around on your website and return to it. It will check who else is linking to you and what types of phrase is used to refer to your website, and the quality of that source. Always think - "why should google trust me" and you'll not go far too wrong.
Inbound links to your website from 1000 other websites of no relevance to your business will count for little. 10 links from "authority" websites such as Morning Advertiser, your pub company, breweries, industry bloggers, review sites etc will be very valuable, and also links from local businesses will help boost your local relevance too.
Every link to your website is seen as a vote. Whether that vote is positive, negative or neutral is what influences your ranking.