Experiment: Many people say it helps to think about taking light field pictures as a whole new art form. Others say most of what they already know about photography still applies.
Get Close: Are you already close? Get closer. If you see a bit of blur, you've got it. Start with thezoom sliderall the way to the left, with the Lytro camera about 6 or 7 inches (15 - 18 cm) away from your foreground subject.
Think in 3D: Compose your pictures with multiple subjects at different distances.
Playing with Zoom : When you do zoom to higher ranges, don't forget "if you see a bit of blur, you've got it" still applies... get close to your foreground subject with your zoom until it blurs a bit.
Steady as she goes: Hold the Lytro camera steady when you take each picture.
Review early and often: Transfer your pictures to Lytro Desktop for review often-- perhaps every dozen pictures or so, at least for a little while-- to learn what works, and what doesn't work.
Practice, practice, practice: The very best way to learn how to take light field pictures is to practice taking them. Have fun!