How does your body know the difference between dominant and recessive genes?

If you have read How Cells Work, you understand the basic idea behind DNA. In a simple organism like an E. Coli bacteria, there is a single strand of DNA. A gene is a section of the DNA strand that acts as a template for an enzyme. The DNA for an E. Coli has 1,000 or so genes -- in other words, it contains the templates for about 1,000 enzymes.

An enzyme is a protein that speeds up a particular chemical reaction. For example, one of the 1,000 enzymes in an E. Coli's DNA knows how to break a maltose molecule into two glucose molecules. That is all that that particular enzyme can do, but that action is important when an E. Coli is eating maltose. Once the maltose is broken into glucose, other enzymes act on the glucose molecule to turn it into energy for the cell to use.

To make an enzyme that it needs, the chemical mechanisms inside an E. Coli cell make a copy of a gene from the DNA strand and use this template to manufacture the enzyme. The E. Coli cell might have thousands of copies of some enzymes floating around inside it, and only a few copies of others. The collection of 1,000 or so different types of enzymes floating in the cell makes all of the cell's chemistry possible. This chemistry makes the cell "alive," allowing the E. Coli to sense food, move around, eat and reproduce. See How Cells Work for details. Any cell is a little chemical machine.

E. Coli cells reproduce asexually. When an E. Coli cell splits, the "child" contains an exact copy of the DNA of the parent. It is a clone of the parent cell.

The DNA in a human or plant cell is different. A human cell has 46 strands of DNA arranged in 23 X-shaped chromosome pairs. One strand of the X comes from the mother, and one strand comes from the father.

Because there are two strands of DNA in each chromosome, it means that plants and animals have two copies of every gene.
Sperm cells and egg cells are unique -- each contains 23 single strands of DNA. When a female creates an egg, or a male creates a sperm, the two strands of DNA in each chromosome must combine into a single strand. When sperm and egg from the mother and father meet, the single strands come together to form new X-shaped chromosomes in the child.
To form the single strand in the sperm or egg, one of the copies of each gene is chosen randomly. One or the other gene from the pair of genes in each chromosome gets passed on to the child.

Recall from the E. Coli discussion that a gene is nothing but a template for creating an enzyme. In any plant or animal, this means that there are actually two templates for every enzyme. In some cases, the two templates are the same, but in many cases the templates are different.

Here is a well-known example from pea plants that will help you to understand the difference between dominant and recessive genes:

Peas can be tall or short.
Tall is normal in the wild. One gene that controls height is a gene that helps produce a hormone known as gibberelline. A normal plant has two copies of the gibberelline gene, so it produces plenty of gibberelline and grows normally.
Occasionally, this gibberelline gene gets mutated. If a plant has one copy of the gibberelline gene that is normal, it still produces plenty of gibberelline. The mutated second gene produces a damaged enzyme that has no effect. The plant grows tall because it has one undamaged gene.
If a plant happens to inherit two damaged gibberelline genes, it will produce no gibberelline, and the plant will be short.

You can see from this discussion that the cell does not "know" that one gibberelline gene is dominant and the other is recessive. The cell is manufacturing enzymes from both copies of the gene. It just happens that the mutated gene produces an enzyme that does not function properly. This has no effect on the plant unless both copies of the gene contain a mutation, in which case the plant gets no gibberelline and cannot grow properly.

Here is are some interesting links:

How Cells Work
How Sex Works
What is a gene, and what is genetic engineering?
How DNA Evidence Works
How Cloning Works
How Human Cloning Will Work