Most genetically modified organisms typically have their genetic material altered, possibly with the material being moved, deleted, or mutated. Mice were the first genetically modified animals, which happened in 1973. Since that time, a plethora of crops and animals have been researched and experimented on for the purpose of making them better or stronger, or different somehow.
The animal may also be altered for the purpose of living longer or becoming more resistant to illnesses. When the genes are linked to a virus and then infected, a host cell then replicates. It will also copy that new DNA, attaching these traits to future cells or offspring.
Another option is to insert the DNA into the nucleus directly. Outside DNA can even be fired from a gun in which plasmid DNA is wrapped around a heavy metal particle and then brought into a nucleus.