There are two main ways something can be genetically engineered.
The first is through direct manipulation. This is accomplished through the use of restriction enzymes to cut out a gene in one organism, and mixing it with DNA of another organism. This method can potentially produce many different strands of DNA, and only a few of them actually have the desired genes. The desired strands of DNA can be identified by using gel electrophoresis.
The second method is indirect manipulation. An example of someone who does this is a dog breeder. Indirect manipulation is selecting genes you want to pass on to the next generation, and actively selecting against all other genes. The different dog and wolf species were created this way, as was broccoli and cauliflower from the wild onion plant.