The genetic structure is the foundation for all of our phenotypic and physiological mannerisms. This phenotype also extends to create the foundation of our mental structure as well, including the basis for the starting IQ and intelligence level. However, the interesting debate is to whether this genetic structure means that we are locked in through our genes to have a certain maximum IQ, or whether we can still increase our intelligence quotient beyond the genetic parameters.
It appears that we can influence significantly beyond our genes. For example, IQ is affected significantly by a person's environment during childhood. If the child happened to have a good level of schooling, a healthy diet and plenty of room for exercise and lifestyle choices, the IQ of the child and person would tend to be higher. In some studies, it is estimated that a child's IQ can be influenced by as much as 30 points through simply factors like playing with the child, food and sleep. This is the case even if the child's starting IQ is particularly low. For example, a child with a starting IQ of 80, can reach an IQ of 120 simply through behavioural and nutritional modifications. Notable studies which confirm this include the Milwaukee and Glenwood Projects.
On the other hand, as the child becomes an adult, the rate of intelligence gains from simple nutritional and behavioural modifications tends to decrease. This is perhaps due to the entrenchment of the physiology on the approach to adulthood. In this case, the manipulation of the entrenched situation is what is needed to boost the mental abilities.
For example, education to maintain mental agility has long been a common way to increase intelligence. Those who have a good education will tend to have an IQ 10-15 points higher than those who do not.
Other notable studies include those done by Southern State University as to the rate of intelligence gains arising from techniques in "The Complete Guide To Genius". IQ gains were measured to be 20-25 points from 35 hours worth of practice. This gain arose through a manipulation of the entrenched physiology which is created by the genetic structure. As such, the genes are not a defining line for the level of intelligence enjoyed by the individual.
To conclude, the role of genetics in intelligence is a small one. The significant factors to influence one's intelligence are the upbringing during childhood, and then the way the intelligence level is used during adult life. Genetics on its own is only a starting point, but not a limiting one as such.