1. Keywords spy
Look for the keywords they are targeting. What I mean by keywords in here is the search words used by visitors to look for a site. For example, if you are a plumber in Sydney, you may want to enter Best Sydney Plumber. Keywords can exists in Meta title and description. You can use Meta Tags Extractor tool to get a meta tags information of a site by entering your competitor site url. Once you have the information, you can simply update your meta tags title and description match closely to your competitor. Please ensure your meta tag title is precise and not longer than 60 characters as Google search will now strip any longer text than 60 characters. Remember to have unique meta tags title and description for all of your pages. Make sure they are not duplicate so Google can determine them as an individual page.
Another alternative option you can do is by targeting another keyword that has less competitors. For example: if your plumbing service only serves couple cities in your state, you may want to include the city name into the keywords like North Sydney Plumber. You can easily use Google Keyword Planner tool to examine how many searches of the keyword you want being searched every month. For any searches less than 200 will have a high chance to secure your site on first page for that keyword.
2. Link Buildings
Start promoting your website by creating links back to your site. This can be done via social media or external blogs that have same or related article contents about your business. Remember due to new Google search algorithm, do not create links back spamming or non related link backs to your site. For example if your business is about plumbing, it is not recommended you add a link back to an article about computer stuff which is not related to each other.
Once this is completed, the next step is to get your competitors links back information. You can exactly do the same your competitors do. Most of the competitors must have place a link back to their site by either commenting an article or suggest a recommendation or even pay someone to write an article and include a return link back to their site. For the commenting and suggestion methods, only apply the links back for the site that has the same topic with your current site. To search the links back of your competitor, you can use this SEO Profiler tool.
Internal links can play important role as well to boost your site performance ranking. This can be done by mentioning to internal page if they have same or similar topic content. If you have blog, you can include some related links to the current topic article.
3. Page Speed
4. Duplicate content
Google dislikes duplicate content. So ensure your site doesn't have any similar content in different pages. Do a redirection if it is required to avoid this. Also take a note on domain www redirection, if you prefer to have www on your domain name, redirect all non www to www in your host settings or server configuration. You may want to ask your site administrator to help you doing this thing.
5. Google Webmaster
Last but not least, sign up for Google webmaster account to find any errors or issues of your site for example broken links etc. Remember to submit your sitemap for faster indexing by Google.