According to the manual, which can be found online here:
http://www.radioshack.com/graphics/uc/rsk/Support/ProductManuals/55041503_PM_EN.pdf, once you start a song using the Play button, you can immediately press the Next button to skip to the next song. It appears that the next button is the right button on the control pad.
Here is the layout of the control pad, from what I can determine online:
Play/Pause
Previous Next
Volume
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