They're making a big push to reach out to new listeners through a contest running from December 15-21, announced on the EVE Online forums. What are they giving away? For starters -- 20 x 500 million ISK instant prizes, 10 x 60-day EVE Time Codes, and 1 Complete Faction Battleship Model set (that's a $500 value!).
But those are only the main prizes. EVE Radio's individual DJs will be running their own events and giveaways. Apparently, all you'll need to do to win is... tune in, and send an Evemail to "MrBlades" when EVE Radio periodically makes an announcement. As they put it: "Once tuned into EVE Radio, you just need to keep your ears open for a special audio alert periodically played during the 7 day event period and then send an Evemail titled 'Giveaway' to the character MrBlades... and be the nth person to do so during that round."
See the full announcement from EVE Radio about their Christmas contest and how you can get your hands on all those prizes, and of course a piece of that 10 billion ISK pie.