As someone who sells SEO as a service it is often not in my best interest to tell people they can do SEO on their own. But it's true. Just as changing the car's oil, fixing clogged pipes, or painting a house are all relatively easy, most business owners can SEO their website on their own. All it takes is some knowledge and time.
Knowledge can be found easily enough for free, and time, well, that's not something you likely have an excess of. Fortunately, SEO doesn't all have to be done at once, it can be implemented a little at a time, as you have time.
If you want to optimize your site yourself then you need to simplify. A lot of what you'll learn about SEO can be complicated. Especially when you start reading about .htaccess, robots.txt, 301 redirects, absolute links, and so on. This is all good information to have but you don't always have to start there.
If you're doing it yourself then start with the things that you can do yourself. Don't get caught up in all the complicated issues that go beyond your knowledge or ability to implement. The more difficult technical tasks may still be necessary down the road, but for now, do what you can with what you have.
Here are some things that you can often do easily enough on your own:
1) Customize all your title tags. If your site is big this may take some time. If its dynamically generated then you may want to have your programmers implement a template that pulls in and inserts keywords based on the page.
2) Customize your content. This can be especially important if you sell products. Don't settle for stock descriptions, and take the time needed to write somethign different for each of the 20 products you have that are simply different versions of the same thing. This customized content is essential.
3) Get content on all of your pages. If you have category pages that link to products or other information pages, put at least a paragraph of text on each page.
4) Link, link, link. Add links throughout your content to other pages and products of your site. Link back and forth between pages, add links to related products, link to your blog and from your blog.
5) Blog. Write content that your visitors will love. Don't just use your blog to pimp your products or services. Write helpful tips and tutorials or provide insight that your readers can use.