We actually have the tech - you just need to manufacture a CO2 scrubbing material and pass lots and lots of air through it. The hard part is the energy - you shouldn't be producing even more CO2 in the process. In other words, getting enough solar / nuclear power, and funding to actually build the thing.

A cheaper alternative would be to pump nitrate and phosphate into some remote ocean, so as to cause an algal bloom. When the algae die, they sink to the bottom of the ocean, and take the carbon with them. But the local ecosystem will be fucked up in all sorts of ways.