How does the Arduino Deumilanove Auto-Reset Function work?
IIRC the cap is wired to /RTS not DTR. 

When /RTS is high there is 0V across the cap. When /RTS goes low the cap 
can not change voltage instantaneously so the reset line goes low. 
The cap charges through the 10K resistor. Once the reset line is above
the reset threshold the uC program starts.

@LouisDavis referenced this page, which states


  The ATmega168 is reset by pulsing its reset pin to GND. ...by setting the DTR line to LOW ... the reset pin gets sucked to LOW until the capacitor is charged through the internal pull up resistor and R1 - which resets the chip.


Simulated:

Auto-Reset
VDTR    1 0 PWL(0 5 0.5m 5 0.000500004 0 1m 0)
Vcc 3 0 5
C1  1 2 100n
R1  3 2 10k
.control
delete all
tran 10n 5m
plot v(1) v(2)
.endc
.END


V(1) is DTR or /RTS and V(2) is /RESET