Work shadowing provides students with an opportunity to gain an insight into a working environment, by observing the duties performed by people there on a day-to-day basis. Work shadowing does not require students to undertake contractual duties which would be performed normally by a paid employee, so you should not expect to be paid.
Typically, work shadowing will be over a short period of time – normally no more than a few days. It provides an invaluable insight into what a job is "really" like (rather than just how it may be described in an advert). It also provides excellent networking opportunities and the chance to impress, which may lead to further, more involved work experience or internship opportunities in the future.