Answer:
   
   Pidyon ha-ben is a ceremony that recognizes the first born male child
   (to be specific, the first born male child that was born naturally).
   The ceremony arose due to the special status of the firstborn in
   biblical society. The firstborn received a double portion of his
   father's estate; the last plague in Egypt killed the firstborn--except
   for the firstborn of Israel. Traditionally, the firstborn of Israel
   were consecrated to service to G-d. The bible commands "sanctify unto
   Me all the first-born (Exodus 13:1). This has been interpreted to mean
   that a father was either to dedicate his first-born son to the service
   of the Holy Temple, or to redeem him by paying five schkels
   (approximately five dollars) to a kohen. Noet that this ceremony does
   not apply when either the father or the mother is of a priestly or
   Levite family.
   
   The Pidyon haben ceremony takes place on the thirty-first day after
   birth. For the occasion, a kohen is specially invited to the house.
   The baby is placed on a cushion, and in the presence of assembled
   friends and family, placed on a table. Five silver dollars are laid
   beside him. In the presence of those assembled, an ancient dialoge
   takes place betwen the father and the kohen. Sometimes there are
   additional English readings, and some ceremonies include participation
   by the mother. The kohen usually gives the "redemption money" to
   tzedahkah.
   
   What do you do if five silver dollars are not available? In the days
   that the Torah was given, the only significance to a coin was that
   someone attested that it contained a known weight of whatever metal in
   question. Thus, any other object of acceptable weight and purity would
   be acceptable (for example, solid silver utensils, such as teaspoons).
   A typical estimate for the weight of a shekel is 11.4 grams, the
   Chazon Ish (a large estimate) has 16.92 grams. You would need to
   consult an appropriate authority with respect to purity.
   
   Pidyon haben is observed in traditional communities, and in the
   Conservative community. It tends not to be observed in Reform
   movement.
   
   Why must the first-born be redeemed? The first-born has a significant
   history in early Judaism:
     * After Cain was born, we're told that Eve gave birth to "Abel his
       brother". Why does Eve define her second child as the first one's
       brother and not a person in his own right? And look how well that
       turned out!
     * We then get to Isaac and Ishma'el, where history sides with the
       younger. Similarly, we see this with Jacob and Esau.
     * First-born issues then cause all that strife between Joseph and
       his brothers (except Benjamin).
     * Next comes Moses and Aaron (and to some extent Miriam), where
       Aaron bows out to give his younger brother the prominent role.
       After we're introduced to Moses and Aaron, we have the plague of
       the death of the firstborn. The Jewish firstborn were saved
       because of the Pascal offering. (Those families where it was
       performed.)
       
   Why is the bechorah (first-born-ness) idea so central that the Torah
   continually returns to it throughout the first book and a half?
   Perhaps because Israel is repeatedly called "my child, my firstborn,
   Israel". Without first drawing a clear definition of the role of the
   first-born, we don't have a clear idea of our national mission.
   
   In Galachah there are actually two kinds of firstborn. It would seem
   that one is a physical primacy, the other a religious one. The
   father's firstborn is the primary inheritor. He gets twofold the
   inheritance of the other brothers. Tribal affiliation, which for all
   the tribes but Levi is tied to the ancestral land, is also
   patrilineal. The mother's firstborn is the one who require's pidyon,
   even if the father had children from another marriage first.
   
   Also, membership in the Jewish people is traditionally matrlineal (and
   is still considered so by the Orthodox and Conservative movements, and
   by most Reform movements outside the US). The mother's firstborn is
   naturally the one to reinforce the religious instruction. It was the
   Egyptian firstborns' failing in this role that made them fitting
   victims of the plague. Not to mention the punishment being in kind for
   the killing of G-d's "firstborn", the Jewish people.
   
   Had there been no history, they would have been the nation's priests
   and (for want of a better word) levites. Just as Israel is called a
   "kingdom of priests" -- which explains the "firstborn" metaphor.
   However, after the golden calf, the majority of the nation was no
   longer trusted to maintain the religion on their own. Only the tribe
   of Levi, who did not participate, were fitting to carry that torch.
   So, they were not given an ancestral territory, and instead given
   tithes that they could live of off. This frees them up to pursue roles
   of religious leadership without worrying about a livelihood. Also,
   without a homeland, they end up more distributed among the flock. In
   the meantime the firstborn, the would-be priests, still maintain a
   vestage of that sanctity. In order to free them from that duty, we
   have the pidyon haben. This redeems their sanctity by giving something
   to their replacements, the kohanim.