They used the Relays, same as everyone else.
To go from one system to another, but as far as fuel and discharging static electricity they would still face these problems. 50,000 ships constantly on the move must use up a fair amount of fuel, and given that they pool credits for ship repairs the Quarians aren't exactly a money rich race. How do you manage to discharge the static of 50,000 ships? I imagine going into orbit with that many would be considered by many races to be a threat.
So either they must have a way around those issues in the 300 years they've been floating in space, otherwise they'd be cooked and/or out of fuel already.