remember that enzymes are proteins so how they are made can be explained by the process of protein synthesis.
1.) The cell receives a signal that loosens the DNA and makes the wanted gene available for transcription.
2.) Transcription: The information provided by DNA is then transcribed into RNA. RNA processing takes place in the nucleus before it leaves for the cytoplasm. This RNA strand is the "messenger RNA" or mRNA for short.
3.) Translation: The mRNA then leaves the nucleus and goes through translation in the cytoplasm. Here, ribosomes meet the mRNA and translates the nucleotides into amino acids. A combination of three nucleotides (codon) = one amino acid. Remember that amino acids are the building blocks of proteins.
4.) The amino acids are then covalently bonded to one another. This produces a polypeptide, another name for protein.
5.) The polypeptide chain will then fold up to accordingly and may go to the rough ER for further modifications and/or the Golgi Body for transportation in/around/out the cell, depending on the protein's function.
After making changes to the protein in the Golgi Body, then the protein is ready to work! Enzymes vary in structure and therefore vary in their function. They can work inside the cell, or they can be secreted.
~David