Generally corals reproduce sexually.  That is a sperm and an egg unite to form the basis for a new organism.  Colonies mainly stay all female or all male.  Supposedly sperms are released in large amounts at a certain time of year into the surrounding waters.  They then find a female polyp in a female colony enter the gastrovascular cavity and fertilize the egg.  The probability of this is extremely low.  This is why corals spend so much energy on the production of sperm and eggs.  The fertilized egg is released as planula larvae.  The larvae spend some time searching until it attaches itself to the substrate and become a protopolyp.  somme coral can produce colonies simply from fragments of old ones.  This is because their reproductive cycle is so short.  This entire cycle can take place within a few hours to a few days.