There's nothing worse than finding that your toilet won't flush, but there's no need to panic as it's easily sorted. Watch this how-to video from Homeserve for a no nonsense guide on how to get your toilet working again.
First off, lift the cistern lid and check that it is full of water. If it isn't, check the float ball, the big plastic ball in the cistern which controls the level of water in the tank. Make sure the float isn't touching the side of the tank and stopping it from rising. If it is, gently bend the flat rod to stop it from doing this. At the same time check that the float rod isn't broken and that the float itself isn't leaking. If so, it'll need replacing.
This can be found right at the bottom of the tank and lifts open to let the water through into the toilet bowl. Yank this up to let the water flow out. If this allows water through then the problem is with the connection from the handle to this flapper valve - more than likely the connection between the lift arm and lift chain is broken and needs to be replaced or just needs a little adjustment.
Is it too loose or too tight? Try flushing and adjust the mounting nut if needed. It may also have become stiff with limescale so give it a clean.
This is connected to the flush handle to the chain. Is it bent or broken? - if so bend it back. Otherwise, you will need to replace it.
This runs from the lift arm down to the bottom of the tank where it lifts the rubbery flapper valve. Check that this is working properly - otherwise this will need to be replaced. It should have about 1/2 an inch of slack, so adjust it by hooking the chain onto a different hole on the handle to get the right tension to sufficiently lift the flapper valve.
After doing these simple checks and finding that the toilet is still not flushing, then give a professional plumber a call to help you sort out the problem. Good luck!