I am writing a novel covering Terraformation and this is an obvious topic to cover. The estimated cost would also be nice as my novel uses many "What if?" situations. The terraformation would create rivers, lakes, and oceans, with winter to tropical climates.
It might be possible but it wouldn't be worth it. You would have to import a lot of materials and the Moon's gravity isn't strong enough to hold the atmosphere. You would have to continuously renew the air.
It only becomes practical (and I'm using that term very loosely) once you can generate artificial gravity on a large scale.
Now if you want to show just how stupidly wealthy you are, you could do it but it still wouldn't be practical.
Think about all the things plants need to survive. Oxygen, sunlight, water, warm enough temperature, and nutrients. Not much of that on the moon obviously! Basically, in order to provide those things for plants to grow one would need lots of energy to do so. That is, energy from the sun or some other source of light, the energy needed to transport the air, water, and energy needed for the heat source. Clearly, one would have to start with growing plants indoors on the moon, and expand from there. Also, like ShadoCat said, there is not enough gravity on the moon to hold the atmosphere in, so one would need to produce more atmosphere than is being lost to space.