You have a couple of options here: You could do this experiment on human subjects, or on an animal model such as mice. Either way, the basic parts of the experiment will be similar.
To try this with mice, you would have two groups of mice, kept in identical habitats and given identical diets except that the experimental group would have a Vitamin E supplement added to their food, while the control group would not. After a period of time on this diet, each mouse would be run repeatedly through a maze. You would time each mouse and see if the mice who got supplemental vitamin E learned the maze faster than those who didn't; you would know this by comparing the time it took each mouse to complete the maze, and seeing whether the times got shorter with repetition. This means that Vitamin E would be the independent variable, and mice's ability to remember the maze would be the dependent variable.
To do a similar experiment with human subjects, you would get a group of volunteers, preferably all of the same gender and age, and randomly assign each person to either the control or experimental group. Both groups would do a memory task, such as memorizing and then recalling a list of ten words. Then the experimental group would be asked to take a vitamin E supplement for a length of time. After the time had passed, both groups would again be given a memory test, and the results would be compare to see if the experimental group's memory had improved.