Outside of South and Southeast Asia, tamarind is usually sold as dense, semimoist pulp in one-pound rectangular blocks; most is imported from Thailand, although a few brands come from India and Mexico. (Whole tamarind fruit, generally grown in Thailand or Mexico and sometimes available in markets specializing in Southeast Asian or Mexican foods, has been bred for its sweetness, not its sourness, and is usually intended to be eaten plain, not used in cooking.) When buying a block of tamarind pulp, make sure it is somewhat pliable; hard-as-rock blocks are likely to be old and stale. Once the package has been opened, seal the leftovers in plastic wrap or slip them into a plastic bag; the pulp doesn't need to be refrigerated and will keep for up to a year.
To make about 1 cup of extract, measure 1⁄4 lb. of tamarind paste (a roughly 2 1⁄2-inch ball) and divide it into 8 pieces. Place the pieces in a small nonreactive bowl and add 1 cup boiling water. Let soak for 20 minutes, periodically mashing the tamarind with your fingers, freeing as much of the pulp as possible from the fiber (and, now and then, seeds). Pour the mashed mixture and its liquid into a strainer placed over an empty bowl. Firmly press down on the tamarind pulp with your fingers until nothing but seeds and fiber are left in the strainer. Discard the remaining contents of the strainer. The tamarind extract may be kept in the refrigerator for up to 2 weeks.