The colonization of Mars has inspired both scientists and science fiction writers for over a century. Even before the Mariner 4 did a flyby of Mars in July 1965 ideas about whether or not the planet could support life had been brewing in the minds of the great thinkers of the era.

Fast forward to modern times, we now know that Mars is a pretty much desolate planet with low atmospheric pressure, no magnetosphere (exposing it to radiation from solar winds) and no liquid water. These facts of course don't stop scientists from making theories on how humans can one day live on the red planet.

Let's tackle your question one problem at a time. Citing the necessary (albeit theoretical) equipment to compensate for the lack of each of these factors:

Water / Oxygen:

It is widely believed that several billion years ago Mars once had plenty of liquid water. Evidence of heavy flooding on the Martian surface has been cited as proof of this concept but where all that water had gone still baffles scientists. Whether it had been absorbed into the ground where it lies frozen or had it dissipated into space when Mars lost its atmosphere. There is still of course wild debate if water is still present on Mars. Recent images from the Mars Orbital Camera has revealed what some scientists speculate as evidence of water seeping out of valley walls and craters from 10 million years to as recent as 10 years ago (the debate still rages on this one as well with some saying that CO2 not water created those gullies).[1][2][3]

These facts notwithstanding, a study of two scientists, Don Sadoway and Ken Debalak how breathable oxygen and drinkable water can be extracted from Mars' abundant supply of iron ore, clay and minerals. Sadoway has in fact designed an electrochemical cell the size of a fridge which is powered by a small nuclear reactor which uses a 450 amp electric current that is passed through Martian iron ore electrolysing them to produce oxygen (which still needs to be mixed with nitrogen to make it breathable) and using Mars' carbon dioxide atmosphere to heated and compressed into until it becomes supercritical which can then be used to extract water from hydrated minerals.[4]

For a planned colony in Mars, expanding and further development of Sadoway's design may one day be used to help humans colonize the planet.

Atmosphere:

Mars has a very thin atmosphere and a normal temperature of 55 degrees below zero (the same as Earth's South Pole temperatures during winter). Even if you create liquid water and oxygen on Mars, without an atmosphere oxygen will just dissipate and water can only exist as solid ice or as water vapor. It has been proposed that the creation of greenhouse gases can be used to warm up the planet enough to coax the carbon dioxide trapped in Martian ice and frost to be released.[5]

An MIT undergraduate, Margarita Marinova has proposed the use of artificially created perfluorocarbons (PFCs) to initiate the warming of the planet. Collaborative research by Marinova and Chris Mckay of the NASA Astrobiology institute has found PFCs to be the best warming agent for use in terraforming Mars. The reasons for this is that PFCs are super-greenhouse gases. A small amount of PFCs causes a large amount of warming. PFCs last a very long time which would be favorable for long term terraforming and it is not harmful to living organisms and does not destroy ozone like CFCs do. [5]

Once enough warming has been achieved, the heat would trigger a natural release of the trapped CO2 in Martian ice further speeding up the creation of an atmosphere.

Food:

Food is the second most important hurdle for a mission to Mars (after funding of course). A manned mission to Mars would require enormous amounts of food which is just impractical to haul along with the mission (USA Today states that the rough costs per pound of launching something into space at $20,000). The proposal is to create greenhouses in which to plant food and help to recycle air as Martian soil is surprisingly similar to garden soil. The problem is that plants recognize low atmospheric pressures as being in a drought and thus cause them to waste precious resources while they try to cope with a non existent drought problem.[6]

Of course once atmospheric pressure has been stabilized on the planet, use of greenhouses for the planting of food is one of the best solutions.

Radiation:

As for the fact that there is no magnetosphere on Mars which then exposes future colonists to enormous amounts of radiation. It has been proposed that the first bases on Mars be constructed underground (as opposed to bringing along radiation shielding) so as to prevent radiation poisoning.

Robotic Development:

Robots and unmanned vehicles have been exploring our known space ever since the space race began in 1957. With further developments of computing and robotic technology it is almost certain that unmanned robots shall be sent to Mars to prepare for colonization years or even decades before the first human even arrives there.

Sources:

http://science.nasa.gov/science-news/science-at-nasa/2001/ast05jan_1/

http://science.nasa.gov/science-news/science-at-nasa/2000/ast29jun_1m/

http://www.universetoday.com/76986/carbon-dioxide-not-water-creating-gullies-on-mars-new-study-says/

http://books.google.com/books?id=nZc5OXn2CvYC&pg=PA125&lpg=PA125&dq=Sadoway+has+designed+an+electrochemical+cell+mars&source=bl&ots=ksQYdFM6Lg&sig=TYTqr1TAYfL_H9i3QjnaVBVSpR8&hl=en&ei=_jJGTuywGMvUmAWRyPyCBw&sa=X&oi=book_result&ct=result&resnum=2&ved=0CB0Q6AEwAQ#v=onepage&q&f=false

http://science.nasa.gov/science-news/science-at-nasa/2001/ast09feb_1/

http://science.nasa.gov/science-news/science-at-nasa/2004/25feb_greenhouses/