If you were to breed a black male guinea pig to a brown female guinea pig in an attempt to determine which one was homozygous dominant and which one was homozygous recessive, how could you be certain that the guinea pigs are truly homozygous?

To make sure they are true-homozygotes, the guinea pigs could be bred for many generations until only one colored offspring were produced.

To discover which color is the dominate, you need to mate a black guinea pig with a brown, both homozygotes,  and see what color the offspring are. Whatever color comes out, that will be the dominant color.

The answer is observations and interpreting.