Begin with a parent that has blue eyes and a second parent with brown eyes. Choose individuals that have only those colors in their family lineage, since you want to make sure both are homozygous; in other words, an individual could have a recessive allele in their genetics that isn't exhibited (this is called a heterozygote). If we used the capital letter "B" to represent brown eyes and lowercase "b" to represent blue eyes, homozygous individuals would have BB alleles for brown eyes and bb alleles for blue eyes. A heterozygous individual would have Bb alleles, but they'd still exhibit brown eyes, making it difficult to assess the outcome of their genetic crosses at this point.
Mate the two homozygous individuals. Since their respective alleles are BB (brown eyes) and bb (blue eyes), the outcome of this cross will reveal all offspring with Bb alleles (brown eyes). Now you have a group of individuals who are carriers of the blue trait, but they still exhibit brown eyes.
Test a second generation by crossing a heterozygous individual with another homozygous individual with blue eyes. If any offspring from this cross exhibit blue eyes, then blue eyes is proven as a recessive trait. The reason for this is that one individual in the second cross had Bb alleles (brown eyes) while the other had bb alleles (blue eyes); so, their offspring could only have blue eyes if they received a b allele from their blue-eyed parent, and a b allele from their brown-eyed parent.