Once you get a volt/ohm meter, you want to start checking the circuits to make sure they are working correctly. I'd check the turn signal circuit first, so go to http://www.nicoclub.com/FSM/G35/Coupe/2005/lt.pdf
page 122. Page 121 basically says to check the fuses, which I'm sure has already been done and it's probably not the problem. Starting at step 2, it tells you what connections to check. If it says check voltage, set the meter to volts, and if it says continuity, set it to ohms.
I'm not sure what you know about electronics, but voltage is how much power is coming through a circuit, while continuity (measured in ohms), is how much resistance there is between two points in a circuit. If you touch the two leads together, you should get 0 ohms resistance (nothing in the way of making a complete circuit). However, if you hold them completely apart, you should get a reading of infinity resistance. If you ran a wire between the two leads, you would get a reading of a few ohms because although the circuit is able to complete, it has to pass through a wire to do so. Make sense?
So anyway, follow the steps to check the turn signal circuit. Connectors M1 and M2 that it says to check can be found here: http://www.nicoclub.com/FSM/G35/Coupe/2005/pg.pdf
on page 42. When you find the connectors, unplug them and stick the positive (red) probe from the meter in the pin # it says to check. Use a t-pin if the connector is too small to get the probe into. The directions also say the color of wire that goes into that pin slot so you can help identify you are on the correct pin #. The first one is pin 11, a Light Green wire and ground (somewhere metal on the chassis). Check with the ignition switch off, accessory, and on positions and compare to the chart. Next is pin 38, a white and blue wire. Etc. etc.
Move on to step 3 if everything seems ok. Do each one of these tests with the brake pressed and not pressed. If everything is working correctly, you should get the same readings either way. I think you may find that you get a different reading in step 3 with the pedal pressed vs. not pressed, but we'll find out.
If you do all that and still can't find any problem, let us know, and we'll move onto testing other circuits.