Windows Media Player:

From the menu bar, choose View → Skin Chooser.  A list of available skins will appear along with a preview of the selected skin.  Choose the skin you wish to use and click the Apply Skin button in the upper left hand corner of the skin chooser.  The player will switch to skin mode.  To return to full mode press Ctrl+1, or click the Return to Full Mode button on your skin.

RealPlayer:

RealPlayer comes only with a default skin.  To acquire new skins, you must download them by choosing View → Choose Skin → Get More Skins… from the menu bar.  A website with skins available for download will appear in the media browser.

After you have downloaded new skins, you may apply a skin by choosing View → Choose Skin and then the name of the skin you wish to apply from the menu bar.