Real Horchata from Valencia is made with Chufa (Tiger Nut). Unfortunately, Chufa is not available (that I know of) in America.
A suitable substitute for the Chufas are Almonds, which give the Horchata the same texture and similar taste. Horchata is not a dairy product and contains little fat, so it is often referred to as "the drink of the gods" for it's rich but low-fat flavor.
From:firstname.lastname@example.org. I'm assuming that you'll start with blanched almonds and will use a food processor to grind them.