SEO is a very wide topic therefore in this article we will have cover the basics and then in later articles we will go into the details.
To google (or any other search engine for that matter) http://example.com and http://www.example.com are completely different websites. You therefore need to decide on one or the other. Once you have, you will to permanently redirect traffic (301 redirect) from one to the other. The specific method to use depends on your hosting environment. Here is a link with a few common methods to achieve this.
The .htaccess file enables directory level server configuration and has several benefits like enhanced security, redirection and much more. You simply enable it by renaming htaccess.txt located in the Joomla site's root directory to .htaccess.
The robot.txt file contains instructions to the search engines on what to index and what to leave out. Include any file or folder you would like to be indexed by simply typing the path to it.
SEO Friendly URLs
Now that your have installed your Joomla website instance, you need to enable search engine friendly URLs. Login to administrator account and go to site -> global configurations and enable the SEO configuration options.
Global Site Meta Description and keywords.
Adding a Meta description and keywords for your website will improve the relevancy of a site's search listings. Set this up in the same section as above.
Content Meta Description and keywords.
These descriptions and keywords provide information about a given Web page, help search engines categorize them correctly. It is therefore best practice to ensure you insert this information for any article that you would like indexed. This section is located to the right of the Joomla article editor.
Add alternative text to all images included in articles.
Adding alternative text for images is the first principle of web accessibility. It is also one of the most difficult to properly implement. Ensure that the alt text is relevant to the picture, so it gives the user a good experience, including the visually impaired. Alt text don't have much weight though in terms of SEO.
Create a website sitemap.
Adding a sitemap is strongly recommended because it will be helpful to both users and search engines. Extensions like Xmap and Joomap make the process very easy. Once the site map is created, create a google webmaster tools account and submit the sitemap. Do the same for other search engines as well.
There are a tonne of ways to do this, from forum post, comments on other websites , guest posting etc. These links show the search engines that your content is relevant and they will rank your content much higher.
This article only seeks to cover the basics of Joomla SEO and is by no means comprehensive. Leave a comment below with the techniques your have used to optimize your website.