Some web designers do include
SEO as a part of their overall package others do not. I would first ask if this is included and if it is, I would ask for some examples from other
SEO work the designer has done.
Specifically I would ask what are the site URLs and what were the keywords that they optimized for each of the pages? From there you can do your own research by testing each of those keywords in Google and check the returned sites to see if their client is in the top 10.
Often time web site programmers are not very good at
SEO and designers are not very good at programming. These skills now are very specialized so you may want to hire a separate person just for
SEO.
Hope this helps!