The recipe from Ishbel isn't at all typical, as it's way more almond than rice. It must be a big hit with gabachos though, because it's the first hit on teh Google for the terms, "horchata + recipe."
If you're here on the left coast -- most Latino places and families make their horchata from powdered mixes you can get at Hispanic supermarkets. The big brands are Maria Elena which is sold as Juanita's (go figure), and Klass. Maria Elena is what you get from the Horchata/ Jamaica/ Tamarindo machines you see everywhere. BTW (or maybe not so BTW) Maria Elena also sells a lot of Jamaica (fruit punch with a healthy dose of hibiscus), and Tamarindo (tamarind punch).
Horchata is one of a class of drinks very popular in the Spanish speaking world called aguas frescas. In Spain, horchata is traditionally made with chufa (melon) seeds. Everywhere else, they use rice.
There are a lot of ways to skin the homemade Mexicano horchata cat, including prep methods and proportions. The basics are rice, water, sugar and cinnamon. Common additions are vanilla, nuts (although not in the same proportions as the other recipe), nutmeg and condensed milk; and, in Oaxaca, pink prickly-pear puree. In Mexico itself, it's not unusual to get fruit in your horchata -- especially melon.
To make it the old fashioned way: Soak the rice and dry flavorings overnight in half the water. Strain the liquid carefully. Dilute with the remaining water and any liquid additions. Adjust for sweetness. Chill well by refrigerating, and stir the mixture frequently because the solids separate. Serve over ice, garnish as desired. For instance, with a sprinkling of walnut or pecan pieces (which I prefer to blending almond into the horchata).
More modern is to use a blender. Do everything the same as before, but thoroughly puree the rice/water mixture in the blender before straining. Otherwise, todo igual (Spanish for alla time same same). You'll get a richer horchata that requires una poquita less stirring.
In a hurry? Add the dry ingredients to half the water, bring to a boil, immediately reduce to a simmer, and simmer for fifteen minutes. Remove from heat, allow to cool for at least half an hour, then puree in the blender, strain, and back to the basic recipe. Result: A still richer horchata with a bit less tendency to separate.
Another variation involves breaking up the rice in the blender before the soak (or cook).
I'll give you typical proportions in amounts that make about a gallon. Adjust them as you like.
2 cups long grain rice (medium or short grain will make a still richer drink)
7 cups water
1/2 cup sugar
1/2 tsp of ground cinnamon
1 tsp vanilla (optional -- but do it)
3 tbs toasted, slivered almonds (optional)
1 can sweetened, condensed milk (optional)
As before. Once you've settled on a formula and technique, the basic proportions will remain, no matter how you multiply for volume.
Hope this helps,