As a Make up Artist it is very important to be constantly updated with the trends, the music scene, fashion scene, different cultures. So part of the job is to buy or consult magazines, books, researching the internet,going to the library.
In London my favorite book shop is RD FRANKS ,you can find everything related to fashion and design!
Another interesting book shop is MAGMA
There are also lots of other book shops along Charing Cross Road, new ones and old ones where you can find real bargains.
Drawing sketches is another Make up Artist duty. It just helps to have an idea of the make up that you want to recreate. If you plan it on paper before, on the day of the job is going to be much easier. It also helps other members of the team (photographer, stylist, etc) to fully understand your idea, sometimes describing the image you have in mind can be hard and can generate misunderstanding.
At MAC cosmetics they have face charts on special paper (you can use eyeshadows on it)which are great for this purpose.
Here some examples of sketches I did for the Moroccan look that I designed for Taktik hair show.