Two phases of SEO
SEO is a two phase process:
Phase 1: Onsite Optimization, it includes keyword analysis, title tag optimization, meta keyword and description, content optimization, anchor, h1 tags, alt tag, sitemap, w3 validation etc
Phase 2: Off Page Optimization: it includes press releases, article submission, social bookmarking, link building etc
You can do everything yourself but you will have to do some reading on all of the above topics. While it can be rewarding if done correctly, it can also black list your website in search engines if you try to use unethical ways of optimizing and promoting your website