The genetics of hazel eyes is not clear yet and has received little research attention. There are only models that try to explain it. One model is explained by Dr. Barry Starr, from Stanford University. However, it is only a model and many others may surface soon.
According to Dr. Starr, a new gene (yet to be found) could be a modifier gene of the gey gene. This gene, named M could produce hazel eyes by having the gey make more melanin. As with any gene, the M gene comes with two alleles, the M which increases the amount of melanin gey makes and the m which has no effect.
Studying the possible combinations of the G (gey) and the M (modifier) genes it would be possible to explain (theoretically) hazel eyes. Anytime you get the G with the M gene you will get hazel eyes (according to this model). So, if a person has the following combinations: GGMM, GbMM, GGMm, and GbMm he (or she) will have hazel eyes. If the person has GGmm and Gbmm he will have green eyes and if he (or she) has bbMM, bbMm, or bbmm he or she will have blue eyes.
Hazel eye color genetics will of course become clearer one day, but for the moment it's models such as Starr's that give us the best insights.
Genetics is also responsible for human characteristics such as blue eyes, blonde hair, and red hair.