Yeah, that's one of the difficulties with WILD - sometimes people just end up falling asleep. This technique in general is more difficult than others, so if you are just starting out with lucid dreaming, I would recommend trying out others as well.

When you are in the stage you described, just stay still until you hopefully start to see more concrete images, and hopefully you will see an entire dream scene appear. When this happens, try to roll off the bed or to stand up... if done at the correct time, you should feel your "dream body" get up while your real body will be fast asleep!