The main problem we face at the moment for this task is the expense of getting materials up the gravity well from the earth. Eventually we hope to find enough water and air on the Moon so we can colonise it, and get to a point where bases would be self sustaining. Further space ships may be then built on the Moon because it has weaker gravity, if places where metal rich asteroids have impacted give enough raw materials.
Eventually this problem is likely to be solved by capturing or visiting nearby asteroids, probably bringing them into earth or moon orbit. These will likely give us all the metals, air, and water we need to build what we need in space. For information on this see cygo.com.
The problem we face now though is that we need to get enough materials into space to send supplies to the Moon to start colonies there, to assemble enough to start the missions to colonise asteroids, and ideally before this to get some sort of presence on Mars or in orbit around Mars.
So the problem we face has a very specific bottleneck, to get lots of raw materials into space now, and these will enable us to get plenty of raw materials later.
The is a way to possibly overcome this specific problem. It comes from the realisation that we already have all of the raw materials we need on the edge of space in our own atmosphere.
The idea is to construct a space ship to go into an elliptical orbit that dips into the atmosphere. This might be a dedicated craft or a space shuttle may be usable. It wouldn't go deeply into the atmosphere enough to get very hot or to get too much drag. As it goes in it scoops up air and stores it in a large container, e.g. the shuttle cargo bay if usable. This air is quickly compressed as highly as possible with the aim of freezing it into solid blocks of frozen gas.
The craft makes as many orbits as necessary to fill its cargo and the returns to perhaps a module on the space station. The thrust needed to do this would be the amount of energy to lift the weight of the frozen gases to the shuttle orbit, and the amount to ovecome the loss in speed from drag with the atmosphere.
When it returns to the space station it freezes the air into blocks like bricks, probably large like a cubic meter each for example. These are used to construct an igloo like shape which is hollow. The blocks are covered with a reflective material so the sun doesn't melt the blocks.
The igloo can act as a radiation shield, to made thick enough for this purpose. The air should also contain Carbon Hydrogen Nitrogen and Oxygen. This is from Oxygen, Carbon Dioxide, water vapor and Nitrogen from the air.
These can be used as raw materials to synthesise plastics which are of course hydrocarbons. Parts of craft can also be made of pure carbon, as carbon fiber. Nitrogen can be used to make fertilisers to start an ecosystem in the igloo.
The igloo has an inner wall constructed that is air tight. This may be just a large bag that contains air and the ecosystem to start making food and recycle air free from radiation. Rocket fuel can be made from water as hydrogen and oxygen, or e.g. methane, etc could be synthesized for thrust. Depending on the thrust needed the craft may just use an inert gas like CO2 heated and expelled.
The advantage here is the raw materials only cost the capital of craft construction and maintenance and the thrust to get them into the desired orbit. Power is all but free and abundant through using tethers and solar panels to make the fuel and plastics, carbon panels, etc.
As long as the craft can bring up more raw materials than it expends in thrust which should be possible through accumulating solr energy the effect is a new accumulation of raw materials in space for little cost when amortised.
When enough is accumulated, like say a cubic kilometer of solid gas this can be propelled towards the moon, by using solar panels and dishes to heat some of the gas to create thrust. Then the block can be dropped into a large crater on the Moon to keep it cold and you have all the materials needed to start a moon base.
Another igloo can be sent on a voyage to various asteroids to bring them closer to Earth at which point the main problem with raw materials will probably be solved. The trip is quite safe for astronauts since there is plenty of air, an ecosystem for food, and protection from radiation.
Another igloo can be sent on a colonising trip to Mars, again powered by solar panels and melting gases for thrust. When it gets there it could connect with one of the Martian moons for extra raw materials and create a permanent base. From there it's a matter of finding a place on Mars with enough air, water, etc. There's little chance of being stranded because of the orbiting base.
I'm actually patenting the idea. The conversions of gases into materials for construction is old technology and well known in establushed patents. The actual cost for construction would probably be converting a shuttle, some kinds of modules on the space station to convert the gases into blocks and then letting the process continue. Of ocurse there are likely to be many pitfalls but the idea seems plausible.
A similar idea was proposed by Arthur C. Clarke to scoop fuel like hydrogen and methane from the atmosphere of Triton I think, but the idea of actual building with the gases and using them as manufacturing materials appears to be new.