On page 15 of the user manual for the 2nd-generation iPod (right-click to download), you get the following instructions for arranging the sequence of songs on a second-generation iPod Shuffle.
1. Connect iPod shuffle to your computer.
2. In iTunes, select iPod shuffle in the Source pane.
3. Click the Contents tab.
4. Click the blank header above the first column to arrange the songs by number.
5. Drag the songs to the order you want.

The problem with that set of instructions is that it neglects to mention that the Shuffle button in the lower left-hand section of iTunes needs to be switched off in order for this to work.

With the Shuffle on iTunes switched OFF, a horizontal line appears when you begin to drag a song on the iPod Shuffle to help you properly position that piece of music in the list.
If iTunes Shuffle is switched on, you will NOT be able to manually drag and re-order the music on your iPod Shuffle, as shown below.

The horizontal positioning line will not appear when you begin to drag the song in this instance.
You must also ensure that you do not sort the list of songs by any column other than the number column, which is the first column, otherwise, you will not be able to manually re-order the songs.
{ 3 comments… read them below or add one }
Your post was really helpful. It helped me get this darn piece of junk to work like i want it to.
Thanks, David!!
Thanks. It really helped me, too! Keep up the good work!
OMG thank you!! It was making me nuts that i couldnt move songs.