There is no magic behind how a search engine decides how to list its results. It is all done automatically through an algorithm based on information taken from the websites. True what information is taken and how the algorithm works is kept strictly confidential and changes frequently, but for the average business there are basic rules which are really common sense. These search results are termed "Organic" and the best sort because they are recognized as being Google's choice and relatively honest.
There are two parts to getting well placed by the search engines.
Your site needs to have content which uses the key words and phrases that most people would use to find your specific type of business or service.
Your website needs to be accessible to the automatic programs search engines use to "read" your site. These programs known as Bots or Spiders crawl through your site on a regular basis and constantly update what the search engine "knows" about your site.
Get these two items working well and you will have the best chance of rating well. Building ion these rules further guidance is available to ensure the best results. So here is the short version of my check list:
The hidden site "meta" key words and description are not directly used by the search engines (they were frequently misused) but having them accurately represent the site and match the site content will improve your sites credibility. So tell the truth and be precise about your meta description and key words.
If your business is local, be sure to register it as a local business with all the web based services, particularly Google. This will almost guarantee your business on page 1 of the local search. Registration is free and easy, so don't get spammed by companies wanting to charge lots of money to do it for you.
The rate at which the engines scan or index your site depends on how frequently you change it. So if you never change the content, you only get indexed occasionally, change it daily and you get indexed much more frequently. This gives you more chance to get topical information linked to your site. You might be thinking "what is the value in me changing the content on my site because my business remains the same" well one answer is that Google can label your site static and stale in which case it will not rate you highly. Remember Google likes fresh topical content.
Search engines also look for links to and from your site. So there is value, particularly if you're a local business, in sharing links to and from complimentary businesses in your area and also links to recognized resources. Not only do you stand a chance of getting referrals' from other local businesses but Google will rate you as a source of local information and having more sites that recommend you.
There is a special type of link to your site known as "Back-links", these are links to a specific article on your site that somebody has used in either a comment or blog. Google really likes these as it uses them to conclude that your content is valuable enough for somebody to reuse and quote you. Getting this type of link is difficult but well worth the effort.
There is another way of getting on the first page of Google, pay for an advertisement. Normally you pay each time someone clicks on your advert and the price depends on the current market rate and can be dynamic at placement. The down side of this relatively inexpensive strategy occurs because Google clearly label your link as an advertisement and plac3e them in special places know for this type of link.
To set expectation about what can be reasonably achieved let's assume you are an honest business in your community with a modern website, this should grant you a first page listing on Google for anybody local who searches for your prime business function. This is because the local search results will favor local businesses, just like the local phone book listings would do. With some reasonable care and attention following the rules you should be able to get in the first couple of local results and rate well for searches for phrases similar to your business name, your specialty and your own name.