Random mutagenesis is the easiest way to change the genome of an organism. In this process, a large collection of individuals of the organism, for example seeds of a plant, is targeted with a mutagen, which is something that damages or changes DNA. The key is to use just enough of the mutagen to cause one change in DNA per unit of organism, for example per seed. The collection of organisms is then allowed to grow or multiply and then screened for changes in a specific activity, also known as phenotype. The individual that shows a new phenotype is then isolated, replicated and analyzed to find out exactly where in the genome the change occurred. This technique has actually been used by humans for millennia. The first farmers used natural error rates in DNA replication as the mutagen and screened potential plants for good phenotypes, such as taste, growth rate, and early germination. These early random mutation experiments are now referred to as 'domestication', and the crop plants grown today are dramatically different from their wild precursors.
Current random mutagenesis is done in a more controlled manner, and much faster than domestication of crops, which took generations of humans to accomplish, and is in fact still ongoing around the world.
Details of the latest random mutagenesis methods are best reviewed using examples from the literature: