How many dominant alleles do you need to inherit that particular characteristic eg brown eyes?

To express a dominant characteristic, such as brown eyes, you need at least one dominant allele. In a diploid organism, which has two alleles for each gene (one inherited from each parent), possessing either one or two copies of the dominant allele will result in the expression of that trait. Therefore, having just one dominant allele (heterozygous) is sufficient to exhibit the dominant characteristic.