After making the Jetpack, it needs to be filled with Hydrogen to run. Hook a Gas Tank up to an Electrolytic Separator and fill it with Hydrogen. Place the Jetpack in the top slot and it should fill up relatively fast (<1 minute). Once full (24000 units of hydrogen) equip it and you should be set to go.
When worn the Jetpack displays the Hydrogen remaining and the mode active in the bottom left corner. There are three different modes, Normal, Hover and Disabled. When on Normal mode, the Jetpack will only use Hydrogen when active. Hover Mode continually consumes Hydrogen to prevent you descending (however you can still go down via the Shift key). Disabled is as it states, the Jetpack will not function.
Lastly, you don't have to worry, the Jetpack will not set fire to anything.
Note : Jetpack can't be worn with a chestplate armor since they have the same slot. But you still can wear helmet, boots and leggings. However there is a possibility given to replenish the loss of potential armor points which would be provided by a chestpiece. The Jetpack is upgradeable to provide 6 armor points, turning into the Armored Jetpack.