Eye shadow can be applied in a wide variety of ways depending upon the desired look and formulation. Typically application is done using fingers or brushes. The most important aspect of applying eye shadow, and makeup in general, is blending well. However, you must not forget to include a primer[1] to limit the chances of creases in your eye shadow later.
To remove eye shadow, a commercial eye makeup remover can be utilized, though a rich face wash will usually remove all traces of color. Generally it is easy to remove, and simple water and soap can be used. Eye shadow, eyeliner, and mascara may also be removed using baby oil. There are also makeup wipes that can be used.