As of now the game does not really give any directions to what parts of your ship actually are.
Right behind your seat will be where the fuel rod is located.


At the back of your ship in the sort of wings is where there are replacement fuel rods, 2 on each side giving you a total of 4 spare rods. You will have to craft new ones if you expend them all.


Press E while having your crosshair over the rod to remove it from the container.


Simple enough just do as you did in step 3, press E with your crosshair over the rod and remove it then chuck it into space!


Now a trick with the rods is that they will need to be aligned when inserted, pressing C while holding the rod will enable snapping, making insertion much easier.
Then just slot it into space and congrats, you can fly again! :)

The generator button you became familiar with in the tutorial can be edited on the fly at any time, we will use this button to optimize the rate at which your fuel rod is expended.


Put your crosshair over the generator button and open your Universal tool by pressing U.
Now it might be a little overwhelming at first but don't worry, it's a lot simpler than it looks.

Line 2 named "ButtonOnStateValue" is what we're looking for and going to edit.
As shown in the video created by fellow community member Stone Legion setting this value to 23 is sufficient to keep your ship running smoothly. Though feel free to experiment to find a value that works for you, that's what this game is all about after all!


Now if all is working correctly you should be able to press the button and see the screen to the right of the button listed "GeneratorUnitRate" slowly rise and stop at 23.000!
Remember to turn this button off when you dismount your ship to save even more fuel :)

As commented by Ghost and HolyCrap the fuel rod can be bolted in place with the Bolt Tool, I assume the rods can also be bolted in place in the racks in the back of your ship. I suspect this makes the rods count as "part of the ship grid" and will be more stable during crashes.

User Krougal commented that expended fuel rods shouldn't be thrown away. The spent rods can be placed back in the racks in the back of the ships for storage.
While I have not gotten far enough personally to test this, there have been mentions that empty fuel rods and be recharged, so they may still have some use later down the line.

Fuel rods can be purchased at the Auction though I've yet to see any being sold.

Fuel rods can be crafted after being researched. You can take a look at the research by pressing K.