For people looking for media planner jobs, you will generally need a (good) degree or HND. Marketing, Advertising, Business Studies, Psychology, Media Studies are all useful degrees to study for media planning. But by no means do you have to have studied one of these.
Why Psychology? Psychology is a useful discipline to use when trying to understand who your audience are.
In order to be good at media planning, you will need the following skills / need to be good at the following: organizing, investigation, creative thinking, strategic minded, communicator (oral, written and presentating), keeping to deadlines, networking, and more.
You also need to be interested in media and keeping up with new developments in this area.
Media planners work closely with people in advertising (media planners are often employed, full-time, by advertising agencies, therefore you need to have a good understanding how advertising works, from the point of view of the account handler, the account planner, the copywriter, the art director, the production team and so on.
You also need to be flexible because media planning has been changing, and continues to change, rapidly.
Lastly, for graduates looking for media planning jobs, you will really need to do some work experience.