Deploy robots and rovers to gather information on atmospheric conditions, gravity, magnetic fields and ice deposits. Robots will be essential to do the heavy lifting of construction necessary to build a base. Robots would be far superior to frail astronauts. Robots can be easily repaired or replaced in a variety of dangerous situations. They require no oxygen, and can also explore dangerous terrain like the ice caps of and lava tubes of Mars. While solar flares and cosmic rays may increase the incidence of cancer for astronauts, robots would be able to work even in lethal radiation fields. In addition to doing dangerous jobs, robots can do dull ones, especially repetitive manufacturing tasks. They can also perform dirty jobs. They can maintain and repair the sewer and sanitation systems on distant colonies. They can work with toxic chemicals and gases that are found at recycling and reprocessing plants. A self-replicating robot labour engine is discussed here.
Send cargo missions with building materials, drilling equipment, solar panels and fuel before manned missions. Another possibility is to send class 4 self-replicating robots that are able to use resources on Mars to start building a base before humans arrive.
Microgravity research would have to be done before manned missions, to mitigate the effect of low gravity on bones and the effects of spending months in space. The solution might be in genetic engineering.
A human expedition finally reaches Mars, making us a multiplanetary species.
Deflection shields would be needed to protect humans from radiation and solar flares due to Mars' thin atmosphere. An alternative is to start building underground by boring tunnels or using underground lava tubes which are natural tunnels. This has the advantage of mining minerals, some for resources and others to send back to Earth to fund more missions.
The red color of the sands on Mars is due to the presence of iron oxide, or rust, so settlers would be able to make iron and steel for construction.
Habitation modules with protection from flares, radiation and dust storms are built. These are eventually upgraded to biodomes, which are closed ecological systems. Cyanobacteria would be used for soil adaptation and the production of food, fuel and oxygen. Fertilizer is essential and its by-products are methane for energy and carbon dioxide for plant cultivation. Deep drilling needs to be done to access frozen, underground water.
Factories such as ore refineries would be built and these would need living quarters for workers. They would make use of advanced robotics for dangerous work and to ramp up production and large scale mining operations. Energy would be from solar power and nuclear fusion plants.
A Phobosspace elevator could be built to boost travel, used to catch and release spacecraft entering and leaving the Martian system. These could greatly reduce the thrust level and fuel quantity needed to go from the surface of Mars to Phobos and to arrive at and leave Mars orbit in a selected direction. This transportation system would lift frequent payloads from the surface of Mars to space at a low cost. Mars would be used as the primary location for support personnel and infrastructure. Phobos would be used as a source of raw materials for space-based activity, and as an anchor for tethered carbon nanotube space elevators to help raise people and payloads from Mars to space. These space-elevators would allow low cost movement of people and supplies from Mars to Phobos and from Phobos to interplanetary space. This approach would allow Mars to be used to support an extensive space industry. In addition, large quantities of material obtained from Phobos could be used to construct space habitats and also supply propellant and material for space industry in the Earth/Moon system as well as on and around Mars.
This would lead to a trade route between Earth and Mars, as well as commercial flights for business and tourism.
Colonists now work and play in cities and use rovers and vactrains for transport. Something like an entomopter could be used for insect-like flight on Mars.
Mars is now a self-sustaining economy with its own currency and government.
The first step to terraforming would be to make Mars warmer for agriculture. Orbital greenhouse heating could be used. A biosphere would then have to be built. By rebuilding the magnetosphere and strengthening the poles, this could rejuvenate water flow that had been held underground for so long.
Eventually Mars would be terraformed and this twin of Earth would make us a true multiplanetary species, putting humanity at a Kardashev scale of ~0.75.