The scenario here is, you want to have a Google Site that contains a Google Doc, where, whenever you edit the Doc, it's automatically updated in the Site as well. Also, you want to make it so that anyone can see it without having to be logged in to our Apps system.
For example, you have a Doc that contains the week's homework assignments, and you want to send your students a link to your Google Site that doesn't change and doesn't require that the students be logged in, so that wherever they are, anytime, they can just visit that link and see the most up-to-date homework assignment. You want to be able to achieve this without having to edit the Site itself all the time.
Here's how. It seems like a lot of steps, but once you go through it once, then you just have to edit that one Doc each week or whenever you need to make changes, and your Site will always reflect the latest changes automatically.
1. Make the Doc. When you're through, click the blue "Share" button.
2. In Sharing settings, click "Change."
3. Choose the option "Anyone with the link" and click "Save."
4. Now, go to your Google Site and create a page to display the homework. Click in the body of the page and go to the "Insert" menu (within the browser window, not your computer's menus.) Choose "Document."
5. Click the document you just made. It'll probably be the first one in the grid, since it's the most recent. Then click the blue "Select" button.
6. You can probably leave the default settings as-is. Click the red "Save" button.
7. When you're editing a site and you insert a doc, there's no live preview, just an ugly gray placeholder; don't worry. Click the blue "Save" button at the upper right.
8. NOW you'll see it as your students will see it. From now on, anytime you want to update the homework, just edit that Google Doc; your Site will automatically show the Doc's contents.