This article is from the Recreational Figure Skating FAQ, by Karen Bryden with numerous contributions by others.
1) Select a flat area which is as sheltered as much as possible from
both sun and wind. Building ice over a nice lawn will make not such a
nice lawn, so it's best to pick an area that you don't mind turning
yellow (more than usual) for the first part of the spring.
2) Construct a border of wood, such as 2x4 lumber, or use mounds of
earth or snow to form a barrier and contain the water. Flatten and
compact the snow in the rink area. Make sure you leave room for snow
to be shoveled off the rink later on.
3) Sprinkle water around the barrier first so that it becomes frozen
solid. Do *not* flood. The main idea is to create an "ice bathtub"
where you can pour water without it running away from you.
4) Then sprinkle water on the snow on the rink. An oscillating lawn
sprinkler works great and will save your hands from freezing! Put on
just enough to make a slush -- this is an important step. If you don't
use enough water then you just get ice on top of snow. If you use too
much water the snow will melt and run off.
5) Once your base has been created, water it well on cold nights and
allow it to freeze between waterings. Continue until you've got an
inch or two of flat, solid ice. Air pockets should be broken and
filled with "slush" to patch them (avoids broken ankles).
6) After the rink has been skated on and the skaters have caused snow
to form, scrape off the snow before adding any more water.