The Basics of SEO can be broken down easily into 2 categories:
First: On-page Optimzation
On-page optimization is the optimizing of a website’s content, text, and titles/headers. The most important of these are the domain name, the title, and the H1 tag. You want to have the keywords you are optimizing for in these spots.
Here is a major rule of thumb: Content is KING! You want to make sure you have totally unique content for your site, as Google hates duplicate content, and you wont ever rank with it. You also want to have a good amount of your keywords in the text of the site.
Second: Off-page Optimzation
This is very important to your site. Google give truth and authority to sites based off of other sites linking to a page. The most links, and the better trusted the links, the better a site will rank. I will get into more details about this, as there are many ways to build links, and this subject is very important.