Tashlich (which translates literally as 'You shall cast'), is one of the rituals performed on Rosh Hashanah.
  • Where:
    Tashlich is recited alongside a living body of water. There are different specifications as to what would qualify, some of them are:
    • It cannot be a stagnant body of water, hence a swimming pool would not be appropriate.
    • The water must have some sort of permanence, a small stream that has no water during dry seasons may not be considered sufficient.
    • The body should have some sort of fish.
  • What:
    The prayer recited at Tashlich is composed of two parts: The first segment comes from Psalms, The rest is comprised of verses from various biblical sources, and includes prayers for/references to G-d's Thirteen Attributes of Mercy.

    A common misconception is that Tashlich requires one to toss crumbs.
    Crumbs of bread are tossed into water...
    (There are, in fact, certain complications which arise from this, as feeding animals/birds/creatures must be done in a specific manner on Shabbat and holidays.)
    dimpster quotes the verse "And you will cast all their sins into the depths of the sea": This is the conceptual background. After reciting the prayer, one is meant to shake out their pockets and Arba Kanfot as a symbolic enactment of the above verse.

  • When:
    Like dimpster says, after lunch on the first day of Rosh Hashanah, and in most communities after the afternoon service, before sunset.
    That's pretty much it. If it is somehow impossible for one to perform Tashlich on the specified day, it may be said throughout the Ten Days of Atonement, even though that's not ideal.
Running water is associated with rebirth and renewal. Given that the Ten Days of Awe are about starting anew, and Rosh Hashanah is the New Year, this is a very symbolic action. We are freeing ourselves of our sins by casting them away. Living water indicates a new start and clean slate.