If you are using the Manually manage music setting, select the shuffle in the iTunes sidebar, under DEVICES. Click the little triangle next to the shuffle, so that it points down. You should see the shuffle's "content" indented under the shuffle.
Right-click on the shuffle and select New Playlist. A new playlist should appear (which you can name), indented under the shuffle. When you drag songs to the shuffle, instead of dragging them to the "overall" shuffle, drag them to this playlist. When you select this playlist under the shuffle, on the list to the right, you can drag the songs around to set the playlist order.
NOTE: If your playlist already appears indented under the shuffle, you don't need to do the above because you have already set up your playlist on your shuffle.
When you use your shuffle, in order to play the songs in playlist order, you need to switch to that playlist. If you play the songs from the All Songs list (with the shuffle set to play-in-order), I believe they play in alphabetical order. It switch playlists, you use the VoiceOver button (press and hold). You can refer to this article for instructions on enabling and using VoiceOver
The sections Changing playlists and To choose an item from the playlist menu explain how to switch between playlists on the shuffle. Even if you only have ONE playlist on the shuffle, there is a separate All Songs list. You must be playing from the playlist to get the songs to play in playlist order.