Recombinant DNA technology adds/replaces DNA in an organism resulting in the recipient organism containing exogenous DNA.
PCR has been a key tool because it permits to amplify sequences.
Plasmids and Recombinant DNA technology
Plasmids are extranuclear fragments of DNA present in some bacteria, which act as a system to transfer genetic material to other bacteria, allowing those to express the transmitted genes. Via restriction enzymes, which cut determinate sequences of DNA in determinate shapes, it is possible to splice into the plasmid a DNA sequence for a gene, and then do not insert it into a bacteria in order to get the product of that gene. The product is the desired protein, and small amounts can be produced in a factory by large vats of bacteria with the not inserted gene.
Note that this system is not valid for advanced cells, as the organization of their genome is different. For these, other systems such as viruses loaded with the chosen material are selected.