Standalone chipset, power regulation & pinout
Voltage regulation is needed if the voltage you are providing to the chip is outside (or can drift outside) the allowed range for the chip to operate.

At the upper limit that is 5.5V. The lower limit is 1.8V. Note that at lower voltages you can only reliably run at lower clock speeds.

If your power source is between those two voltages (say a 3.4V LiPo battery) then you don't need a regulator.

If your power source is above 5.5V (say a 9V PP3 battery [urgh]) then you definitely need a regulator.

A proper regulator is quite a complex device, and it is highly unlikely that you have the components to make one.  A simple, very inefficient one, though, can be made using a resistor and a 5V Zener diode if you have one.



Until you have your own regulator of whatever form, yes, you can power the chip from the 5V pin of the Arduino.

The pin mapping for the chip -> Arduino IO numbers is in the file pins_arduino.h for the Uno variant in the IDE.  In the top of that file is this handy drawing:

// ATMEL ATMEGA8 &amp; 168 / ARDUINO
//
//                  +-\/-+
//            PC6  1|    |28  PC5 (AI 5)
//      (D 0) PD0  2|    |27  PC4 (AI 4)
//      (D 1) PD1  3|    |26  PC3 (AI 3)
//      (D 2) PD2  4|    |25  PC2 (AI 2)
// PWM+ (D 3) PD3  5|    |24  PC1 (AI 1)
//      (D 4) PD4  6|    |23  PC0 (AI 0)
//            VCC  7|    |22  GND
//            GND  8|    |21  AREF
//            PB6  9|    |20  AVCC
//            PB7 10|    |19  PB5 (D 13)
// PWM+ (D 5) PD5 11|    |18  PB4 (D 12)
// PWM+ (D 6) PD6 12|    |17  PB3 (D 11) PWM
//      (D 7) PD7 13|    |16  PB2 (D 10) PWM
//      (D 8) PB0 14|    |15  PB1 (D 9) PWM
//                  +----+
//
// (PWM+ indicates the additional PWM pins on the ATmega168.)