When I was in college, there was a fraternity on campus that made a skating rink on their front lawn every winter (this was in Troy, New York). Basically, they hosed down the snow on the lawn and let that freeze to get a hard surface. Then they would lay water on top in thin layers so it would freeze quickly, until it was smooth -- instant skating rink! The cold air and ground temperatures were enough to freeze the water and keep the ice solid for several months. Then, in the spring the whole thing would melt and they'd get their lawn back.
That doesn't work so well in Florida. Indoor skating rinks almost always use cold concrete to make the ice. When the rink is built, miles of metal pipes are laid inside a concrete slab. A large refrigeration plant (see How Refrigerators Work for a description of the refrigeration process) produces ice-cold glycol that runs through these pipes. The entire slab of concrete that makes up the arena floor drops below freezing. Then, thin layers of water are poured on the concrete and allowed to freeze.
The lines and logos at a hockey rink are literally painted onto the ice. Then, more ice is added on top of the paint to protect it.
Here are some interesting links: