To learn about playlists see the bottom half of this thread: How to transfer music to my iPod (& iTunes)
To play a song from the main part of your library just select it & press the Launch button. Remember the play button only works with the playlist.

Also remember that a playlist is simply a reference file that has a list of titles & points the player to their location. If you move the songs after having created the playlist, then the playlist won't work.