Unclogging a loo is no ones idea of fun but a huge bill from a plumber is not either. It can therefore be well worth trying to sort out the problem yourself.
Before you start take some precautions, put on some old clothes, rubber gloves and protect the floor with some paper or old cloths. The loo may overflow or splash and so it is good to protect the flooring and make clearing up afterwards that bit easier.
The first main tip is to not keep flushing to loo. If it is blocked and you try to flush it again, it may then overflow. So the first thing to do is to turn off the water supply to the toilet.
There are several things you can try. You can put some washing up liquid down the loo (just a few squirts and then put half a bucket of hot tap water in to the pan. Make sure the water is hot but not boiling as this could crack the pan. Pour the water from high up as this may help it to push down heavier. If the water level goes down after a few minutes then you should be able to flush the loo and get rid of the blockage. If not then you will need to use a plunger.
Make sure that you get a good quality plunger. A rubber one with a bell shape of rubber flange on the bottom are best as they are more likely to work and ta larger one is likley to be better. If it is too small, when you push it down the water may come up the sides of the toilet bowl and this will not achieve anything.
When you put the plunger in, make sure it is in the water and you push down slowly and firmly. If there is not enough water there add more as you need to be plunging the water and not the air. Pull it up sharply and then push in slowly – do not push too hard as it may jam the blockage down further. You may need to do this a few time to loosen the jam and allow it to move freely down the drain.
If this does not work you can try using a wire coat hanger. Unravel the hanger and then put one pointy end down the loo and move it around to try to unblog it. You can buy a plumbers snake which will get further down the loo if this does not work. It does a similar thing.
If you have a wet/dry vacuum then you could try vacuuming out the clog.
You can buy a variety of chemicals and enzymes in hardware stores which you could use to try to dissolve the clog but it will depend on what the loo is clogged with as to whether they will be effective.
If none of this works then you will need to call a plumber.