When you look at a rocket on Earth's surface, you're looking mostly at fuel and vehicle, with a little payload on top. In contrast, for the vehicle that lifted the Apollo astronauts off the Moon, the fuel required was so little that it fit in a corner of the vehicle and the fuel tank could have served as a chair. The key to space development using asteroidal and lunar materials is the ability to make the fuel propellants from these materials, rather than blasting the fuels up from Earth. Extracting this oxygen from lunar soil is fairly simple, and the processing schemes generally aim to produce other useful materials, too. The hydrogen is rare on the Moon except at the lunar poles where it exists in extremely cold form.
Many asteroids are rich in frozen water, and oxygen-hydrogen rocket fuel is readily producible.
Asteroids are also rich in carbon, too, which can be used in rocket fuels, e.g., hydrocarbon fuels. Many lunar development schemes propose using substitutes for the hydrogen, e.g., powdered aluminum, which would still be mixed with oxygen for combustion. Aluminum powder based engines have been researched dating back to the Apollo days when NASA planned to develop the Moon, but the technology hasn't been developed yet for in-space applications and indeed has been shelved without an application in today's Earth launch world. The first step is in production of hydrogen and oxygen is extraction of water from the asteroid. All that's needed is to deploy a solar oven, e.g., an array of foil mirrors focussed on a tank.