To obtain a job working in the engineering and scientific departments at NASA, you should attain a bachelor's degree or higher in a field specifically related to the type of occupation you are seeking. Degrees in aerospace engineering, biology, computer engineering, computer science, general engineering and meteorology are all applicable to jobs in this sector.
NASA is a large agency, employing almost 19,000 salaried workers and even more independent contractors. As with any organization of its size, there is a lot of administrative work to be done. Having a degree in business administration or management, computer networking or communications will help you secure a job working in one of NASA's many administrative positions doing public affairs, budgeting, contracting or information technology work.
With almost 20,000 on-site workers, and the potentially dangerous nature of some of the work they do, NASA has to have a few medical professionals on board to take care of any emergencies or work-related illnesses. Getting a degree and license in nursing or medicine will get your foot in the door doing medical work for NASA, while having a degree in electrical or mechanical engineering will help you snag a position doing technical work for the agency.
At the heart of every organization are the clerks. Every boss needs a secretary, every office needs an accountant, and every manager needs an assistant. These jobs do not mandate a particular degree, but having one never hurts your opportunity to advance. If you are looking to get a job doing clerical work for NASA and hope to advance from there, consider getting one of the degrees specified for other NASA positions and vying for a job from within. This will give you an edge over candidates fresh out of school with no NASA experience.