geiger tube dc power supply
This site is an excellent reference in everything geiger-countery you might ask. There's a nice schematic which shows the complete circuit, including the power supply and the detection parts:


In general you just need a Mohm-range resistor to limit the current through the tube, and a few transistors/resistors (the "impulse detection" part).

After that it's just simple arduino code (attach interrupt, etc.)