Nothing is perfect when it comes to plumbing first things first ensure your stop tap turns off (go check it now before winter) they often seize up and you can't turn it off (plumber job of it won't often need replacing and needs isolation in the street to replace)
So it works good
So most houses are plumbed in good old copper (new builds are often plastic Aka speed fit or PEX )
Standard copper size is 15mm or 22mm
So it's minus 5°c 6am and your awoken by water dripping through the bedroom ceiling (been there had it happen ) frost has frozen the water in the pipe burst the copper as dawn broke the temperature rises the ice melts and well drip drip drip.......
First thing make safe turn off the electrics .... water and light fittings / junction boxes can make your hair stand on end
now been on here take 20 mins to select a torch 
and go turn the stop tap off.....Depending on your home you might have a BIG water tank to drain in the loft / airing cupboard ... Empty the sink and turn the taps on full of it's a tank supplied cold / hot water system to drain the water flush the loo anything to drain the system and reduce the escaping water to a minimum. If it's a leaky radiator shut off the valves at each end ... If pipework locate your drain cock turn off the boiler cobble the garden hose onto it and open the drain and open a few bleed points on the radiators upstairs .. ours drain points are opened with a radiator bleed key .... Some use a 8mm spanner eg
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But what if the water won't shut off
Speaking to a plumber by the time his client Google's his number he gets a phone call puts some pants on and rushes over and charges his emergency call out fee
well the ceiling is usually down and a insurance claim is needed .....Now this isn't a Infallible method but could help mitigate and reduce damage ..
A few tools are needed most are cheap the 15mm pipe cutter cost me £6 the 22mm is also £6 (well £5.99 if your going to be pedantic) and a push fit "service valve" £5 ISH each for both 15mm and 22mm this is a minimum kit so £22 ISH for 4 items and a £1.50 scotch pad ideally
Obviously access is issue if the burst is close to a joist you need to take a educated guess as to the direction of flow you need to cut the supply side of the leak... Pipe supplies the bathroom tap.... Cut the side of the burst away from the tap
So we have a burst pipe spirting water out
Demo pics:
Stop tap won't work (or turn it off if it does) either way open all the taps this should reduce the pressure at the burst if it's on the mains water circuit and send a fair chunk of water down the drain.... If it's the heating system turn off the boiler / pump
Use the rough scotch pad (car shops sell them for removing paint get the corse one (red) to clean the pipe on the supply side of the pipe
You need to be about 2" ideally 6" from any joist on the supply side you will see why ... And have the ability to cut about 1 ft from the outlet end
Now pack the area with towels / blankets / whatever is to hand.....
I like the fixed size over the adjustable ones for emergency work ensure a minimum of 1" clean copper on the supply side and have the valve to hand with it open !
Why? Try shoving that on the pipe against water pressure
By now water will be to put it bluntly pissing out the pipe under force the cutter gives a nice clean cut with no burrs unlike a hacksaw which is important speed fit uses an o ring to seal.. so it won't rip the seal likewise cleaning the paint off ensures it seals well
Now grip the pipe that's spitting water and with your other hand grip the push fit valve and push them together firmly till it stops then yank the new valve back a bit as you do the lock ring pulls back a bit
Then rotate the valve to shut off the water...
Now you need to towel yourself dry and mop up as much water as possible
And ring the plumbers
As a true diyer I also have some PEX pipe end fittings and some other none valve inline connectors and pipe cutters .
Remember saying about cutting about a foot out above
Cut some PEX pipe about the distance between the new valve and the push fit inline connector ends add on the length of the 2 push fit inserts before cutting ( one for each end) as that's the amount that sits inside the new fittings
Ideally you need a bit of free play in the original pipework of about 1 1/2 inch to slip in the new
pipe
But ultimately..
You will now have 2 speed fit ends a bit of pipe prepped to fit between the 2 fitting ends and a permanent fix
It's worth checking if your putting plastic in place of copper you might need to add a earth (cpc) cross strap to ensure earth continuity of your water / central heating system throughout the house
any issues with my work will expose an argument over out of date smoke detector bases (they have a date of expiry on them. I've got enough knowledge and qualifications to cost them a fortune if they get clever . 
) 