Supplying +5v to Mini. 4th pin from top left here is +5v.
Reset pin is 3rd from left here. This goes to earth when the push button is used. Held high, normally, through a large resistor.
This is the Mini's digital pin 13. We connect an LED (and resistor) in order to get some visual debugging. The LED should flicker briefly immediately after releasing the reset pushbutton, or after powering on.
Not pictured: USB cable to computer.
It's really connected to +5v. This large (10kohm) resistance allows us to connect reset to +5v AND, when the reset button is pressed, to ground, without making a short-circuit between +5v and ground.
The reset switch. The connections on the diagonals of this momentary-press button are normally open, and form a circuit when pushed. The arduino kicks off again on the rising edge when you release this button.
without this resistance, too much current would run through the LED and it'd die.
Mini ground pin is here 3rd from left, on bottom. Should be the same as your arduino NG's ground.
Tx - connect this to Tx of the Arduino NG, and Rx (right) to Rx of the NG, remove the NG's atmega chip, and then you can program the mini via the NG's serial-USB connection. Just remember to tell the Arduino IDE that you're using Atmega168, via the Tools:Microcontroller menu.
Rx. See Tx on left.
remove this chip when you're ready to program the Mini via this NG board.