Of course, the most important thing on the list is Content. With no content, or improper content, your site won't be trusted by the Search Engines. A similar situation to a website with no/incorrect content is a Radio Ad with no sound, or just static. Not only won't listeners (visitors) know what is going on, but they won't have any reason to return.
Keywording, though less important than content, will still help the Search Engines find your site. They are there so that the robots indexing the internet have an extra reassurance that your site's content is what you say it is. Users can't see it, but Search Engine Robots and browsers can.
As for linking, this is another way Search Engines build trust in your site. An example of how this works is if your site deals in Vegetables: a trustworthy link would be from a nutrition site that explains the benefits of vegetables. This would increase the trust that the search engines place in the site and up your rankings. A link that isn't as helpful would be from Ginger Ann's "Favorite places on the Net" site (does not actually exist, I made that up). While this doesn't build trust in your site, it is still helpful to have a link. More links tell the Search Engines that your site is more popular.
SEO involves more things, obviously, but these are the main ones that we here at TJ Design Studio will start with when your site needs SEO.
Check the SEO category of our blog for more information!