Assign a letter to each gene pair. Each parent has two chromosomes, and therefore two of each of the four genes. The two members of each pair are not necessarily identical. Different variants of a gene are called alleles. The easiest way to choose letters for each gene pair is to go in alphabetical order, where the first gene pair is A, the second is B, and so on for the four pairs. An offspring receives one allele of a given gene pair from each parent. If the alleles are different, one may be dominant and the other recessive. An upper case letter is assigned to a dominant allele, and a lower case letter is assigned to a recessive allele.
Write out the genotype for each parent. The genotype is a list of the alleles that parent possesses. Genetics test questions or homework problems of this kind will give you the genotype of both parents, so you'll have that to work with, and the letters will already be assigned. Since each parent has two copies of each of the four genes, the genotype will be eight letters long--one letter for each allele of the four genes. An example genotype might be AaBbCcDd, where the parent has two alleles of each gene--one dominant, the other recessive.
Draw a square and divide it up into a grid of 16 columns by 16 rows, so that there are 256 boxes in the square. The boxes should all be the same size. This is your Punnett square, and you'll use it to depict all the possible results that could occur from the cross. See the second and third links in the References section for examples of what Punnett squares look like.
Write down all possible genotypes of the gametes each parent could produce. A gamete is a sperm or egg cell. Remember that while the parent has two copies of each gene, each gamete a parent produces gets only one copy of each gene, because sperm and egg cells only have one set of chromosomes. Consequently, a gamete will get one copy of each of the four genes, but it could get either allele from each of the four pairs, so there are 16 possible combinations. If the parent has genotype AaBbCcDd, for example, the gamete might get only the four dominant alleles (ABCD), it might get the four recessive alleles (abcd), or it might get some dominant and some recessive (AbCd, ABCd, etc.).
Write down all the possible genotypes contributed by one parent along the top of your Punnett square, one genotype per column. Write down all the possible genotypes contributed by the other parent down the left hand side of the Punnett square, one genotype per row.
Fill in all 256 boxes of the Punnett square by putting the genotype for that column together with the genotype for that row. If the genotype for the row is ABCD, for example, and the genotype for the column is abcd, the box at the intersection of that column and row would have genotype AaBbCcDd. Once all the boxes in the Punnett square have been filled out, you will have a complete list of all the possible genotypes that could be produced by this cross. The Punnett square can be used to calculate the probability that an offspring will have a given genotype. Count up the number of squares that have an identical genotype and divide that number by 256 to get the probability that an offspring will inherit that particular genotype.