This device uses the new levitation potion effect.  

To use jet boots, you need both the jet boots, fuel,  and the flight controller.  Both of these can be "floor crafted" with the below material:

Jet Boots
2 redstone repeaters
1 redstone comparator
2 blaze rods
1 pair of golden boots

Flight Controller
1 redstone torch
1 eye of ender
1 compass

The fuel is simply a fire charge.  One fire charge will give you 30 seconds of flight.
WARNING: IF YOU RUN OUT OF FUEL OR DISABLE JET BOOTS IN MID AIR YOU WILL MOST LIKELY DIE FROM THE FALL NO MATTER HOW LOW TO THE GROUND YOU ARE.  TO FIX THIS, SIMPLY LAND BEFORE DISABLING THE JET BOOTS OR RUNNING OUT OF FUEL.

To use the flight controller, equip it into your off-hand slot and look up to go up, forward to float where you are, and down to descend.  After selecting which Y direction you want to go, you can swap out the flight controller with and eye of ender and you will continue to fly down/up/stationary no matter where you look. In short, both the eye of ender and flight controller will activate the jet pack, but the flight controller allows you to change whether you go up, down, or stay where you are.  

This one command creation was made using MrGarretto's command combiner: http://mrgarretto.com/cmdcombiner