Getting your website to rank in the search engines does not take as long as you think. There is really only 3 major parts of your website that you need to be worried about when optimizing for search engines. As long as you have optimized these parts correctly, you should move up the search engines fairly easily.
Keywords are the most important part of SEO. The first thing an SEO company would do is an analysis of your site to find out what keyword category you fall into. That way, they can get an estimate of much search traffic you can receive if you decide to use certain keywords on your site. Not every keyword gets the same amount of traffic so you want to make sure that you select the keywords that are most relevant to your business, but still high traffic.
Now that you've got your keywords, let's use them. Content is the new way the top search engines are starting to rank websites. Most search engines do not look at your site like a viewer might do but they look at the words on your page. The search engine spiders gather all the words that you have typed in on your pages or pictures that you might have posted that have titles and alternate text in them. They measure how much density each words has and they make you rank based on how many times those words came up on your site compared to a competitor's site. Make sure that you have plenty of keyword rich content on your page so that the spiders will see you as relevant for a certain topic or keyword.
Some people say that links are going away but I do not think they can ever really go away completely. Back Linking has been a way that search engines have ranked sites for years. That's how they can tell how popular someone is or if they are an authority on a certain topic or product. If you get links from popular websites that have a high page rank, you get power from that. If you can get power from the highest ranking websites online, you will rank higher in the search engines. Only build high quality links to your site and make sure that they are relevant so that you do not get seen as a link spammer. Post articles, make blogs, build websites, and link back to your website.