Step 1: Realize That the Illum Is Not a Point and Shoot
A big misconception with the illum is that you can just point it at something and click. While this is true to some extent, you wont get the nice,sharp image.
Always "fully" focus on one plane of your shot. If you are shooting with a foreground and a background make sure that you get a nice focus on the foreground, thats what people pay attention to.
Step 2: Plan Your Shot
Sure, you could use your illum for regular landscape photography but that would be a total waste. To really take advantage of the lytro illums living pictures you need an interesting foreground and a beautiful background.
When your out in the field, make sure to look for branches, fence posts, stones or other protruding objects that would make an interesting shot. Preferably the object should be centered and take up 1/3 of the image.
The picture above is a "still" from a living picture i took a couple of days ago you can find the "live" version here.
I would consider this one of my best lytro pictures: it has multiple planes, good focus on the foreground and a good foreground-background ratio.
Step 3: Use the Lytro Button
The lytro button lets just see what the camera detects as foreground and background. The blue represents foreground and the orange background. You adjust this by changing the focus. Slowly turn the focus "wheel" until your happy. You want alot of both orange and blue for a sharp looking image.
If you see a blue and orange dots jumping around in the image you need more light, adjust the iso or turn on a lamp.
Step 4: Use the Lanyard As a Hand Strap
So this might just be me, but i dont like to have my camera swinging from my neck and scratching up the screen when i walk. My big dslr has a nice hand strap, but because of the illums anchor point standard hand straps cant be used. What you can do is to mount both sides of the lanyard to the top anchor point.
Now you can easily wrap it around your hand and have a secure grip of your camera.
Step 5: Adjust the Depth Map
Along with all the info a normal camera gives you, the illum has a depth map. The depth map shows how close things where to the camera when the picture was taken. In good lighting conditions the depth map looks fine but if you shoot in low light conditions you might have to adjust the depth map.
The depth map can be adjusted by going to the "adjust" tab in the lytro desktop app.
Thats it! Now go out and take some awesome living pictures!