Goldfish need to be conditioned to spawn. This usually means a period of a month or so at a cool temperature and proper feeding before and after this dormancy break. People in temperate climates with ponds have no trouble spawning their fish. Once the water temperature rises towards 68 degrees Fahrenheit (20 degrees Celsius), usually spawning activity will begin. Goldfish typically spawn in the wee hours of the early morning.
My fish showed no signs of spawning until I gave them some spawning material; then, within 12 hours they were at it. I used a green nylon mesh I purchased at a fabric store (tip: guys with weird projects get lots of attention from the women who work at fabric stores). The advantage of the mesh was that it could be sterilized and reused, and that it allowed excellent water circulation around the eggs. The only downside was that it seemed a bit abrasive on the pectoral fins of the female as the male drove her through the material.
I hand spawned the fish initially and then let them naturally spawn after that for 4 or 5 hours. This gave me two sets of eggs, which I raised separately for the first few months. All I knew about hand spawning was what I had read in books; I was able to do it, but I think I injured the female in the process. What happened was that some of her vent parts everted during the stripping process. She recovered and seemed fine, but then died suddenly 3 months later during some water quality problems. I believe this loss very possibly could have been related to the earlier injury.
Goldfish eggs are very adhesive once wet. Based on a method suggested by a Belgian veterinarian in the goldfish Internet mailing list, I stripped the female of roe into a small dry dish. I then stripped some milt from the male into this dish. Then I mixed the roe and milt together thoroughly. I had spread some of my nylon mesh in the bottom of a clean 55-gallon tank; I swirled the contents of the dish into the water and allowed the now-adhesive eggs to sink down and adhere to the mesh. This gave me a nicely scattered distribution of the eggs. I then moved the mesh to a 10-gallon tank for hatching, put fresh mesh in the 55, and put the pair of Ranchu in to spawn naturally. Which they did with enthusiasm.
Above: Goldfish eggs on nylon spawning mesh ("thule" from a fabric shop). The opaque white eggs are infertile. The rest will hatch in a day.
In both tanks with eggs I put a drop per gallon of methylene blue. This is supposed to reduce the severity of the fungus that develops on infertile eggs. If this fungus gets out of hand, it will start to kill adjacent fertile eggs. I had no trouble with fungus developing. This water was gradually changed out as the fry began to hatch.
Ultimately I would estimate I got over 8000 eggs: 2000 from the hand spawning, about 5000 from the natural spawning, and 1000 in assorted other places. The hand-spawned eggs were about 95% fertile and the naturally spawned were about 50%. Needless to say, this resulted in a lot of fry.