By the way the lighter looks a little odd because I can't find my real zippo, this is a very similar bomblighter, which works just fine for demo purposes.
The original - Basic Zippo Tricks
My second round - Zippo tricks 2
Learn how to reflint and rewick your zippo.
As always: Video...
Step 1: Palm Squeeze and Light
Now your middle finger should push on the top corner of the lighter on the opposite side from the hinge, if you're having trouble take a look at the photos, to make sure you have it right because it's not that easy to explain.
Now push the lighter in with your middle finger allowing it to catch on the webbing of your fingers, with this one pressure isn't the key, it's more about getting a continuing motion.
Now bring your middle finger round and light it.
Flick your wrist back to close the lighter.
Step 2: Gun
Hold your hand out, fingers straight.
Put the zippo in between your thumb and palm. The hinge should be facing down your arm.
Bring your other hand back across the zippo, palm down, fingers out, the underside of your knuckles should come across the lighter, the front of them knocking it open and the flintwheel hitting somewhere around the middle.
Flick your wrist forward to close.
Step 3: Slide It.
Open the zippo and set on the table, use a finger to press on the flintwheel, the further you want it to go the harder you press before letting it roll over.
Thanks to the windowsill being a bit rough my lighter fell forward. I also combined black magic or the twilight zone in to the slide. Because I had noone to slide to.
Step 4: Break and Light
The hinge goes against your middle finger and your index and ring fingers go on the lid and body - the body should be under the index finger.
Bend your middle and index fingers, the ring finger will stop the lighter from flying away, as it comes round in to your palm strike the flintwheel with your thumb.
To close you can move your ring finger from the lid and flick your wrist to the side. Alternatively just roll your ring finger over to close the lid.
Step 5: Smack Light
Hold the Zippo between your fingers and thumb, index finger on the lid.
Lift the zippo up, opening the lid with your index finger, set your finger on the flintwheel on the way down.
When you hit your other hand/table/leg the finger will roll the wheel and light the lighter.