Fiona,
It all depends on what type of integration you want to achieve. It is best to first review the information available in the online FAQs.
You can create a new folder in the local copy of your Web site (on your computer) and have Shozam generate the gallery in there. This will allow you to use Expression Web to upload the gallery together with your site. However, you should generally not edit the gallery files outside of Shozam because the next time you use Shozam to update your gallery, it will overwrite your changes.
The best type of integration is done using Shozam Business Edition to add custom HTML code to your pages (on the HTML tab in Step 5) which allows you to insert at the top of every gallery page the same type of masthead you have elsewhere in your site.
The simplest type of integration is to just link from your Web site to the URL of the gallery and have it open in a new window. When the viewer is done, they would close the gallery window and thus get back to your main Web site.
And then there are other options in between. If you have Shozam Advanced Edition, you can create navigation links at the top of the gallery pages (Step 5 --> Link tab) that a user can click on to get back to your main "home" page on your Web site.
A solution that can look elegant but technically is not recommended (not only that it requires some more HTML knowledge but it is also deficient in terms of having your gallery extra optimized for search engines) is to create a page on your Web site for your gallery (using Expression Web), place an IFRAME (inline frame) in the middle of the page (where you want your gallery to appear) and point the IFRAME to the location where your gallery is online.
Take your pick; you should find a solution that works for you depending on the Shozam edition you have, the technical skills you possess and specifically what you envision as an end result.