Making an existing website search engine-friendly is a bit like trying to make an old volvo more aerodynamic.  You might have some success, but the best results are achieved if it is considered at the very beginning. 

Search Engine Optimisation (SEO) begins with YOU.  When you are considering the text for your website, think about the words people are likely to search for.  It sounds obvious, but it is important to ensure that these words appear in the text, in the headings (where possible) and in the page titles.  Don't overdo the keyword density though or your could get penalised.    

To do well in the search engines write your copy for PEOPLE (not computers).  Websites in the past used to engage in keyword-stuffing, but search engines soon wised up and changed the way they rank sites to give a higher ranking to pages which supply good, informative content.  If you are working with a copywriter, check that they are aware that you are targeting search engines for particular words but make sure they write for your customers.  Ensure that your graphic designer also understands which words you are targeting so they don't create designs which require the words to be converted to images. 

When constructing your menu, try to name your pages according to the words you are targeting as this will give them added weight. 

If you follow these techniques you will be on your way to a good organic search engine listing.