Genetic engineering is a procedure by which foreign genes are inserted into an organism, or existing genes are altered, to modify the function of living things. The basic technique of genetic engineering is very simple. Certain proteins, called restriction enzymes, have the ability to cut a DNA molecule so that the DNA has several unattached bases at the cut end. Think of those exposed bases as something like pieces of Velcro at the ends of the DNA strands.
If another strand of DNA is cut in the same way, and if the exposed base pairs on that second strand are complementary to the base pairs on the original strand, then when the two strands are put together the bases will bind and the strands will stick together. This procedure allows researchers to take a stretch of DNA , cut it, and splice in another stretch of DNA that has the appropriate base pairs on it ends. The new DNA will contain an extra stretch of genetic information in it.