Have you designed the voltage step-down aspect of your circuit yet? The typical approach is to throw a linear regulator between 12v battery + and the 5v Arduino input. Good practice would be to put a large reservoir cap on the 12v side, then 0.1 to 0.3uF caps on both the 12v and 5v side as close to the regulator as possible. Also a 0.1uF next to the ATmega chip.
It might also help to have a diode on the 12v side to make sure voltage is always flowing the right direction. If you do it like this, it'll prevent your reservoir cap from discharging through the pump when you turn it on:
| + |*----* >| *----*-----*----*--> LM7805 IN
| | ^DIODE^ | |
| BATT | 100uF > = = < 0.1uF
| | | |
| - |*--------------*-----*-------> LM7805 GND
Pardon the crappy ASCII schematic.
EDIT: Woops.. just a few minutes late. ;-) "What he said."