How do I get iTunes to just play one album?

It's rather easier than these solutions. Click the icon view beside the search and select the Albums tab at the top so the icons show albums rather than Artists or Composers. Then when you hover over an album you can click "Play Album" to play it. You can also double click the album to see all the songs making sure they are ordered by song number (if necessary).

This way you can also by command or shift clicking select multiple albums.

Or you can show with the second icon ordered by album by artist. In this view an artist search will help:

You can go to the menu bar and select View » Column Browser » Show Column Browser. Then you can pick an Album in the third column, and only songs on that album will appear in the iTunes window. Note that this will switch you from the Grid view to the List view.

While in List view you could:

• If using Play Random Song, just search for the name of the album, and play. Unless you clear the search box, the played songs will be the ones from the search.

• If you're not using it, just order the list by Album and play the first song. The rest of the album will play afterwards.

You could, too, create a new PlayList, drag all the songs from that album, and play.