The study of the subject of SEO is actually akin to the Job Description of a Website Administrator. As you can probably appreciate, if the Website Administrator actually did his job properly in the first place, there would be little need to further optimize the site for the search engines. The more SEO a site requires, the less effective the site administrator is.
This is false only if all site administrators in that field are experts. Website Administration should not to be confused with Website Marketing. Administration and Marketing are two totally different fields and require different approaches from two totally different educational backgrounds. Yes, it is true that an effective administrator or a skillful entrepreneur can make for easier marketing. But we are not talking about that it factor here. As in you either have it or you don't.
SEM (Search Engine Marketing) or SEA (Search Engine Advertising) skills involve drawing traffic into the website through paid advertising (eg. adwords) or affiliate programs (where a commission is paid for sales that originated from warm leads [traffic] provided from affiliate websites). There are also some of other menial tasks any admin can allocate to the post which you can find in many available expanded definitions of SEM or SEA.
Some try to tell you that the seo and the sem/sea are the same function, they are not. It is like saying a web designer can do all the functions of a web developer. The training paths are different. Either can have a natural talent for the other area but without training, this is usually an exception, not a standard.
Proper seo requires a much greater level of technical skill compared to those required of an sem/sea. The SEO is more likely to have a science/maths background where as the SEM/SEA is more likely to have excelled in various studies of the social sciences. An SEO should be able to perform the technical functions of an SEM/SEA but the reverse is not true.
To be truly successful with SEM/SEA, one should have some grammar, computer skills and exposure to formal studies that approximate the subject of Behavioral Targeting. Formal training will come to mean a double degree in Tech and Psych.
In other words, those that would be a natural at SEM/SEA are entrepreneurial types or those with a bent for fields in applied psychology (preferably business related) and have a good handle on the grammar of the language of the site. The application of "if, then, else" for the SEM/SEA is not the same as what the better SEO would have studied.
And just as the designer complements the developer, the SEM/SEA compliments the SEO. But the SEO or Developer can get a game going with out the presence of it's complement. If i am talking to the business owner here, you should be the person who knows best on how to sell your product. You then make the SEO put your instructions into practice for you or you learn how the seo goes about doing that and do it yourself.
In short, you would save a lot of money by hiring an seo first. The seo would (could, should) fix the technical aspects of your site so that traffic can flow into the site without any change in advertising expenditure.
If there is no change in web page hits, he then rethinks the presentation of your content (eg. too much flash, graphics, layout or inappropriate wording).
When this is corrected, you will be be positioned to reap benefits from any skillful marketing campaign that uses online marketing strategies. And of course, you will cover some of these seo techniques right here and now so that you can immediately increase your market share by applying what you learn as you go.