That is not quite all.
SEO is a bit more complicated than it used to be and the above is slightly outdated info. Agreed that paying stupid prices for other companies to do your
SEO is a waste of money, however that is if you have the time to do it yourself.
First place to start is with Google Webmaster tools. It is free and will provide a lot of tips to get your site search engine friendly. You also need to have well written content that is relevant. No good just slapping the keywords in everywhere with hidden links.
Once you have your site sorted, then you need to build
good quality back links to your site. This can take time.
With every Google update, the algorithms become more advanced and can weed out sites that "take the piss" and try to manipulate search engines. If you get it wrong, your ranking can be lowered or worse case, you can get slapped and removed from search engine ranking altogether.
It's not hard, just need to spend some time and have patience. Even with agressive
SEO, the results can take a few weeks to filter through.