Hydroponic plants get oxygen from the plant root uptake. Oxygen is provided particularly as dissolved oxygen in the nutrient solution. This occurs in zone of aeration that is provided by a gap from the exterior to the reservoir water level. Check out http://www.homehydrosystems.com/nutrients/oxygen_page.html for more particulars.
Plants can also get oxygen though the water. Plants need carbon dioxide though... they MAKE oxygen. We should think of that next time someone clears a field to put in another Super WalMart. I would rather have the oxygen.
Hydroponic plants get oxygen by absorbing the dissolved oxygen (DO) in their nutrient solutions, which is vital for the health and strength of the root system as well as being necessary for nutrient uptake.