First find out about the medium they are using. Each medium has its own properties. Silverpoint is delicate, even ethereal, and technically demanding. You can achieve a similar look with a fairly hard pencil kept very sharp, and a light touch. Chalk can be soft and atmospheric, but was often used with a great deal of precision. Ink is used with a flexible dip-pen that allows for some variety of lineweight. Often pen drawings of the old masters have a degree of freedom and energy that makes them seem almost modern in comparison to the restrained detail in their oil paintings.
Traditionally, a study of the old masters would be conducted on a Grand Tour of Europe, but for those of us who weren't born into the Landed Gentry, there's Wikimedia. You can find loads of public domain reproductions of old master paintings and drawings. Quality varies, but many are at printable resolutions. Even tracing (using your monitor as a lightbox) can be a useful exercise to help you train your hand to follow shapes. Try tracing some guidelines and then copy the rest of the drawing, trying to match the lineweight and direction of the artist's linework.
More experienced artists might like to try creating their own drawing in the style of a favorite artist. You'll need to think about the characteristics of their work: subject, viewpoint, lighting, line, tone, gesture... Try setting up a photograph to look like the subject in their work, and using that to draw from.
More on Old Master Drawing
Drawings on Wikimedia Commons
Leonardo da Vinci
Hans Holbein the Younger