Why not power the arduino from the same 5v supply? Connect it to the 5V header pin.
Decoupling - put 0.1uF/100nF on each pins power pin. Nothing to work out. Very standard.
Base resitor - most times transistors are being used as switches. You want to turn them full on or full off.
For NPN/PNPs: need to limit current out of the Arduino. Voltage across the Base to Emitter is usually around 1 Diode forward voltage, ~0.7V.
So (Varduino - Vbe)/35mA = lowest resistor value to be used. (5V - 0.7V)/0.035 = 123 ohm, so a 150 ohm will work nice. No lower than 120.
For N-Channel/P-Channel Mosfet - these take very little current, but can have high gate capacitance. So a 150 ohm in series will prevent Arduino pin damage as the capacitance charges up. A 10K pulldown (N) or pullup (P) transistor will keep the gate low while the arduino boots up and the pin floats prior to the sketch driving it high or low.
Multiplexing - this is easiest to see with a picture.
One common method is to have the a,b,c,d,e,f,g anodes of multiple displays connected in parallel. The common cathode from each device is then controlled seperately. Drive the anodes, drive 1 cathode. Drive the anodes, drive the next cathode. Repeat. Cycle thru all of them fast enough so the eye doesn't detect flickering.
For an n-digit display: 8 anodes, n common cathodes.
MAX7219/7221 controls this for 8 digits, refreshing at an 800 Hz rate.
Can also be paralleled cathodes, and n common anodes.
Charlieplexing - this Maxim application note provides a great description.http://www.maxim-ic.com/app-notes/index.mvp/id/1880
Charlieplexing - only 9 pins to drive 8 digits.
MAX6951 does this for 8 digits.
I don't know that any one specific book will cover everything.