In order for a baby to have blue eyes, BOTH parents must have the gene for blue eyes. Both parents might have brown eyes, though. This is because, as I said above, brown eyes are dominant and blue eyes are recessive.
For example, if the mother and father of the baby both got a blue eye gene from one of their parents and a brown eye gene from the other parent, they will each have both genes..........the gene for blue eyes and the gene for brown eyes. In this case, there is a 75% chance that the baby will have brown eyes and a 25% chance that the baby will have blue eyes.
Going further, if the baby gets a brown eye gene from EITHER parent, the baby will have blue eyes. However, if the baby gets the blue eye gene from BOTH parents, then the baby will have blue eyes. Since there are 4 possible combinations of genes, and three of them involve a brown eye gene and brown is dominant, threee out of four will have brown eyes.
Just for completeness, the 4 possible combinations are:
Brown from mother, brown from father, baby will have brown eyes
Brown from mother, blue from father, baby will have brown eyes, since brown from mother is dominant over blue
Blue from mother, brown from father, baby will have brown eyes, since the brown from the father is dominant over blue
Blue from mother, blue from father, baby will have blue eyes
This is why 2 blue eyed people can NOT have a brown eyed baby. If the parents both have blue eyes, we know that they both have 2 blue genes, so all that they can pass on the baby is a blue from the mother and a blue from the father, and the baby will ALWAYS have blue eyes. If the baby has brown eyes, and we know that the mother has blue eyes, then we also know for sure that the father has brown eyes.
Sorry if this is too much information, and sorry if I am causing you any troubles with paternity or anything like that, but this is all true. Don't take it for gospel, though, as I am a dentist, not a geneticist, and, before you make any decisions, you should probably consult a geneticist. Perhaps there are exceptions.