Burst or badly leaking pipe
Turn the water off at the mains stop tap — usually at the front boundary near the meter. Turning it off stops the damage even though it does not fix the pipe.
Burst pipes, sewage backing up, no water at all. Call and describe it — you will get a straight answer about what to do and when someone can be there.

Brigs Plumbing's Google profile is set to 24 hours and the phone is answered around the clock. That is a promise about the phone being picked up, not a promise that someone is already in the van at 3am — what you will get is a straight answer about how soon somebody can be there, and what to do in the meantime.
For a lot of after-hours calls, what to do in the meantime is the most useful part. Knowing where the mains stop tap is, and turning it off, stops a burst pipe from doing thousands of dollars of damage while you wait.
Detail
Turn the water off at the mains stop tap — usually at the front boundary near the meter. Turning it off stops the damage even though it does not fix the pipe.
Stop using every fixture in the house, including the washing machine. Every litre that goes down adds to what is coming up. Keep people and pets away from it.
Turn off the isolating valve on the cold inlet to the unit, and switch off its power or gas supply at the isolator.
Check whether neighbours have water too. If the whole street is out it is a supply issue and the water authority is the right call, not a plumber.
Do not touch it. Switch the affected circuit off at the switchboard if that can be done safely, and say so when you call.
Questions
The phone is answered around the clock. Whether someone can be on site immediately depends on where you are and what is already booked — you will be told honestly rather than left waiting on a maybe.
Yes, as with any trade. You are told the price before work starts, at night the same as during the day.
Usually at the front boundary near the water meter, sometimes in a small covered box in the ground. Finding it now, while nothing is wrong, is worth five minutes of a Saturday.
Call. The contact form is checked in business hours; an emergency needs a phone call.
Nearby
Describe the problem on the phone. If it can be sorted without a visit, it will be.
Licensed plumbing, drainage, pipe relining and roof plumbing across Brisbane and the surrounding councils — Redland, Logan, Moreton Bay and Ipswich. Based in Thorneside.
QBCC licence 15161521
Member, Master Plumbers’ Association of Queensland
ABN 44 526 011 279