If your toilet is blocked:
Blocked toilets are usually caused by something blocking the system, and will need to be unclogged. Flush the system once, and use a plunger to gradually pump the blockage through the system. Avoid flushing the toilet too much while it is blocked, as this will cause an overflow.
There is no blockage, but the flush mechanism will not work:
To diagnose the issue of a non-flushing toilet, remove the cover on the back of the toilet to view the flushing system and make sure the flapper element is attached and working.