I think it could be done in one of three ways.

One, we use our conscious thought to move the water one molecule at a time, this can be accomplished by getting the entire human population to focus their intention on moving the water to mars. Note that there is mounting evidence that shows that water is effected and can be manipulated by thought alone.

The second way is to move the water with our dams, this in conjunction with the moon's gravitational pull. This can be done at the precise calculated moment when there would be enough gravitational pull to at least pull a city sized glob of water from earth's surface, and if done at the right moment, would land perfectly on the martian surface. The only problem is that all life on earth would have to go underground or in live in space stations because the surface of the earth would be completely decimated.

The third option is literally manufacture water on mars. But that raises extremely interesting and conflicting notions; as to who owns the water and who gets to do what with the manufactured water.

Whatever the case, each is highly political; with the prayer and intention manipulation being the least devastating.