I've never had to remove it from a civic but it's pretty much the same for most vehicles.
Remove the lines, compressor, ac bracket (if separate- I think civics are combined with the steering pump bracket) and condensor. The evaporator is buried within the dash so you can leave it in place and never notice it is there.
http://www.freeautomechanic.com/airconditioning3.html
There's a basic page for info about AC units in cars.
You should probably take it to a shop and get the whole system discharged first since it is pressurized freon and very bad to breathe. Then unbolt everything and pull it out at home.
Do it without damaging the parts and you'll be able to get some $$ back out of them on ebay since AC is a high priority in the south.