Take a look at http://www.cathodecorner.com/bikeboombox/ showing the system in detail.
The amplifier circuit board is of my own design. It uses a Texas Instruments Class D stereo amplifier chip to provide 15 watts per channel of clean sound with very low battery drain. I designed a circuit board with everything needed for a nice bike system, including a charging port for your MP3 player.
The amplifier board details are http://www.cathodecorner.com/bikeboombox/cdamp/
Step 1: The components
The amplifier circuit board is available from my one-man company Cathode Corner for $100 assembled. you may also download all the design info from my website and build your own if you are good at surface-mount assembly.
The 6" sewer pipe is available from any big plumbing supply house (not Home Depot or Lowe's, unfortunately) but needs to be cut carefully, a task that I describe how to do.
The bike rear rack is available at any decent bike shop. You may already have one on your bike.
A fully assembled CDAMP amplifier board with angle brackets
A battery pack, Li-ion 18650x4 series cells with protection circuit (Batteryspace)
A 14.4V Li-ion charger (Batteryspace)
A 5.5mm/2.1mm DC power plug to fit the amplifier board (Digikey or Mouser)
A pair of Kenwood KFC-1652MRB marine speakers (eBay)
Two each .250 and .187 quick-disconnect crimp terminals to fit the speakers
Three feet of two-conductor speaker wire, 18 to 22 gauge
A rear bicycle rack, standard aluminum type (local bike shop)
Two feet of 3/4" Sch. 40 PVC electrical conduit
18" length of 6" Sch. 40 ABS sewer pipe (big plumbing supply house)
One foot of 3/4" to 1"x1/8" 6061-T6 aluminum bar stock (hardware store)
A dozen #8x3/4" sheet metal screws
Two 8-32x1/2" machine screws, flathead preferred
Two 6-32x3/8" machine screws, nuts and lockwashers or nylock nuts
Electric drill and/or drill press
Fractional drill bit set, up to 3/8"
Countersink, #8 screw head
#1 and #2 Phillips screwdrivers
Sharpie marking pen
Small file, square or flat
(optional) Large miter box or the parts to make one and a crosscut saw