The standard way to do this is to apply a special lense onto your camera whilst your filming.

However if you do not have a special lense or you need to convert something that is not filmed, such as a animation then you have to find a plug-in/converter for a program.

The main program i am using is Adobe After Effects so i needed to find a plug-in for this program. Luckily i was given a plug-in by one of my course mates called "fulldome". This creates the effect of a fish-eye lense.