When it comes to the fuel requirements it's not so much the distance, it's the speed.
Here is what is called a delta V map of the solar system.
If you look at the map you can see the earth to the left, and lines with a value. This value is the delta V, or total acceleration, required to reach each point.
In spaceflight delta V is a measure much speed your velocity has changed by burning propellant in your rocket engine. It is also a measure of the amount of effort required to move between different orbits.
To see how much delta V is required to get from Earth to the surface of the Moon you simply add up all the numbers along the way.
According to the map it takes 9 km/s of delta V to get to from the surface of the Earth to low Earth orbit. From here on, we just need another 5,67 km/s and we are on the surface of the moon.
So let's say we have a spaceship with an astronaut in it, and we have a rocket capable of putting it in low earth orbit. But we want to go to the Moon! Since we need 63% more delta V we make the rocket 63% larger.
Now we shoot our brave astronaut to the moon! Our spaceship reaches earth orbit. Onward to the Moon!
Unfortunately we don't make it to the surface, nor do we make it to lunar orbit. The rocket doesn't even make it past Lunar transfer.
Our rocket ran out of fuel somewhere before geostationary transfer and our brave astronaut orbited the earth until he ran out of supplies and died.
This is because the tyranny of the rocket equation. The rocket equation is a formula that can be used to tell you how big your rocket needs to be to attain a certain amount of delta V for a given payload. As a quick back of the envelope calculation we can simply assume that the rocket doubles in size for every 2 km/s we want to add. So to get our spaceship to the surface of the moon we will need a rocket that is 7 times larger than the rocket that took it to Earth orbit.
But wait! We can't leave our astronaut on the moon. He must get back! So we go back to earth, adding the numbers along the way. Fortunately we don't have to go all the way back as we can aerobrake after moon transfer, and we only have to add 2,54 km/s of delta V.
Our moon rocket is now 17.2 times larger than our original low earth orbit rocket, and a whopping 390 times larger than the tiny little spaceship that is launching.